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@nmayorov
Last active November 15, 2017 21:32
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LC phase transition Monte-Carlo simulation
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from matplotlib import pyplot\n",
"from itertools import product\n",
"from numba import jit, float64, int32, optional\n",
"from numba.types import Tuple\n",
"import numpy\n",
"from scipy.special import eval_legendre"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Монте-Карло моделирование состояния нематического жидкого кристалла"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Введение"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"За основу взята статья 1972 года \"Nematic-Liquid-Crystal Order —A Monte Carlo Calculation\" авторов P. A. Lebwohl and Q. Lasher, опубликованная в Physical Review A."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Для моделирования нематического ЖК методом Монте-Карло рассматривается трёхмерная прямоугольная решетка, в узлах которых находятся стержневидные молекулы. Состояние $i$-ой молекулы определяется единичным вектором ориентации $\\nu_i$ её оси. При этом, каждая молекула взаимодействует только с шестью ближайшими соседями, и энергия взаимодействия двух соседних молекул определяется формулой:\n",
"$$\n",
"E_{ij} = -\\epsilon P_2\\left(\\cos \\theta_{ij}\\right)\n",
"$$\n",
"\n",
"Где $P_2(x) = \\frac{3}{2} x^2 - \\frac{1}{2}$ --- полином Лежандра второго порядка, $\\cos \\theta_{ij} = \\nu_i \\cdot \\nu_j$, $\\epsilon$ --- максимальная энергия взаимодействия."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Полная энергия системы находится суммированием энергий всех попарных (среди соседей) взаимодействий. Вероятность системы находиться в данном состоянии определяется распределением Гиббса:\n",
"$$\n",
"p \\sim \\exp \\left( -\\frac{E}{kT} \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Для создания выборки из такого распределения предлагается использовать метод Монте-Карло по схеме марковских цепей. А именно алгоритм Метрополиса-Хастингса по следующей схеме:\n",
"\n",
"1. Последовательно перебираются молекулы в узлах решетки.\n",
"2. Для каждой молекулы вычисляется ее энергия взаимодействия с соседями в текущей ориентации и в новой ориентации, которая выбирается случайно равномерно. Пусть эти энергии $E_p$ и $E_n$.\n",
"3. Если $E_n \\leq E_p$, то новая ориентация молекулы сохраняется.\n",
"3. Иначе, если $E_n > E_p$, то новая ориентация сохраняется с вероятностью $\\exp \\left( \\dfrac{ E_p - E_n } { k T } \\right)$. Это выражение --- ни что иное, как отношение вероятностей нового и текущего состояний (нормировочные константы сокращаются, а вклады остальных молекул в энергию взаимно уничтожаются в разности)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Стартуя этот процесс из некоторого начального состояния, требуется провести некоторое количество итераций, до момента, когда начнут генерироваться состояния из желаемого распределения, а исходное состояние уже не оказывает влияния. Когда процесс сойдется к желаемому распределению, можно посчитать среднюю энергию и параметр порядка, как простое арифметическое среднее по состояниям."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Реализация процедур"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Решетку молекул будем представлять в виде 4х-мерного массива, где в последней размерности длины 3 хранится вектор ориентации. Для равномерной генерации вектора на единичной сфере (вектора ориентации), нужно сгенерировать 3 числа из стандартного нормального распределения и нормировать получившийся вектор к единичной длине.\n",
"\n",
"Функция реализующая создание случайной решетки:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def generate_random_lattice(width, height, depth, random_state=0):\n",
" rng = numpy.random.RandomState(random_state)\n",
" lattice = rng.randn(width, height, depth, 3)\n",
" norm = numpy.linalg.norm(lattice, axis=-1)\n",
" return lattice / norm[:, :, :, None]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Реализуем функцию, которая вычисляет энергию приходящуюся на 1 связь. Всего существует $3 N$ связей, где $N$ --- число молекул. Для вычисления энергии решетка циклически сдвигается на 1 индекс вдоль каждой из пространственных осей (что соответствует периодическим граничным условиям), далее вычисляются скалярные произведения и энергия взаимодействия вдоль данного направления. Значение энергии максимального взаимодействия между двумя молекулами $\\epsilon$ в этой функции полагаем равным 1, либо считаем, что вычисляем энергию в единицах $\\epsilon$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def compute_energy_per_bond(lattice):\n",
" energy = 0\n",
" for axis in (0, 1, 2):\n",
" lattice_shifted = numpy.roll(lattice, 1, axis=axis)\n",
" cos = numpy.sum(lattice * lattice_shifted, axis=-1)\n",
" energy -= numpy.sum(eval_legendre(2, cos))\n",
" return energy / numpy.product(lattice.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Реализуем вычисление параметра порядка. Для этого нужно сформировать симметричную матрицу \n",
"$Q = \\frac{3}{2 N} \\sum_{i = 1}^N \\nu_i \\nu_i^T - \\frac{1}{2} I$ и вычислить ее собственные значения и векторы. Параметр порядка равен максимальному собственном числу, а директор --- собственному вектору, соответствующему максимальному собственному числу."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def compute_order_tensor(lattice):\n",
" nu = lattice.reshape((-1, 3))\n",
" return 1.5 * numpy.dot(nu.T, nu) / nu.shape[0] - 0.5 * numpy.eye(3)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def compute_order_parameter_from_tensor(order_tensor):\n",
" w, v = numpy.linalg.eigh(order_tensor)\n",
" if w.ndim > 1:\n",
" return w[:, -1], v[:, :, -1]\n",
" else:\n",
" return w[-1], v[:, -1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Для реализация процесса Монте-Карло моделирования нужна также функция, которая вычисляет энергию взаимодействия молекулы с ее соседями. Т. к. она будет вызываться часто, то ее нужно реализовать в виде компилируемого кода. Есть разные способы добиться этого в Питоне, здесь я использую jit-компилятор проекта numba, который позволяет получить скомпилированный код из обычного питоновского кода, добавлением простых аннотаций типов. В теории он должен работать также быстро, как код, написанный, например, на C."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"@jit(float64(float64[:, :, :, :], int32, int32, int32, optional(float64[:])), nopython=True)\n",
"def compute_energy_at_site(lattice, x, y, z, direction):\n",
" if direction is None:\n",
" direction = lattice[x, y, z]\n",
" \n",
" width, height, depth, _ = lattice.shape\n",
" energy = 0\n",
" for x_new, y_new, z_new in [((x + 1) % width, y, z),\n",
" ((x - 1) % width, y, z),\n",
" (x, (y + 1) % height, z),\n",
" (x, (y - 1) % height, z),\n",
" (x, y, (z + 1) % depth),\n",
" (x, y, (z - 1) % depth)]:\n",
" cos = numpy.dot(direction, lattice[x_new, y_new, z_new])\n",
" energy -= (1.5 * cos**2 - 0.5)\n",
" \n",
" return energy "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Реализуем функцию, которая будет обновлять состояние решетки согласно описанному алгоритму. В качестве параметра, который определяет температуру системы, используем $\\beta = \\epsilon / (k T)$, т. к. видно, что только от него зависит распределения состояний.\n",
"\n",
"Функция также будет ускорена с помощью numba.jit. При этом состояние решетки и тензорный параметр порядка перезаписывается (обновляется \"in-place\"), а функция возвращает только изменение энергии (приходящуюся на одну связь). Кроме того, новая случайная ориентация молекулы и случайное число от 0 до 1 передается в явном виде, подразумевается, что эти числа будут сгенерированы предварительно."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"@jit(float64(int32, float64, float64[:, :, :, :], float64[:, :], int32, int32, int32, float64[:], float64),\n",
" nopython=True)\n",
"def update_state(n_molecules, beta, lattice, order_tensor, x, y, z, new_direction, rand):\n",
" old_energy = compute_energy_at_site(lattice, x, y, z, None)\n",
" new_energy = compute_energy_at_site(lattice, x, y, z, new_direction)\n",
" \n",
" delta_energy = new_energy - old_energy\n",
" if delta_energy < 0 or rand < numpy.exp(-beta * delta_energy):\n",
" order_tensor += (numpy.outer(new_direction, new_direction) - \n",
" numpy.outer(lattice[x, y, z], lattice[x, y, z])) / n_molecules\n",
" lattice[x, y, z] = new_direction\n",
" else:\n",
" delta_energy = 0\n",
" \n",
" return delta_energy / (3 * n_molecules)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Реализуем функцию, которая будет проводить Монте-Карло симуляцию. Она принимает начальную конфигурацию решетки и делает `n_passes` проходов по всей решетке. При этом вычисляется и сохраняется энергия и тензорный параметр порядка каждого состояния."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def run_monte_carlo(lattice, beta, n_passes=1, random_state=None):\n",
" lattice = lattice.copy()\n",
" \n",
" width, height, depth, _ = lattice.shape\n",
" n_molecules = width * height * depth\n",
" n_transitions = n_molecules * n_passes\n",
" \n",
" energy_all = numpy.empty(n_transitions + 1)\n",
" energy_all[0] = compute_energy_per_bond(lattice)\n",
" \n",
" order_tensor = compute_order_tensor(lattice)\n",
" order_tensor_all = numpy.empty((n_transitions + 1, 3, 3))\n",
" order_tensor_all[0] = order_tensor.copy()\n",
" \n",
" if not isinstance(random_state, numpy.random.RandomState):\n",
" random_state = numpy.random.RandomState(random_state)\n",
" \n",
" new_direction = random_state.randn(n_transitions, 3)\n",
" new_direction /= numpy.linalg.norm(new_direction, axis=1)[:, None]\n",
" rand = random_state.rand(n_transitions)\n",
" \n",
" i = 0\n",
" for pass_ in range(n_passes):\n",
" for x, y, z in product(range(width), range(height), range(depth)):\n",
" delta_energy = update_state(n_molecules, beta, \n",
" lattice, order_tensor, \n",
" x, y, z, new_direction[i], rand[i])\n",
" energy_all[i + 1] = energy_all[i] + delta_energy\n",
" order_tensor_all[i + 1] = order_tensor.copy()\n",
" i += 1\n",
" \n",
" return lattice, energy_all, order_tensor_all"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Численные эксперименты"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Сходимость алгоритма к распределению"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"В указанной статье написано: \n",
"\n",
"> We determine the thermodynamic and statistical quantities of interest by averaging over the lattice configurations generated after the system has reached equilibrium. For temperatures far from the transition, only one run, consisting of 2000 different lattice configurations on a 10x10x10 lattice, was necessary;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Из этой фразы не очень понятно, что они подразумевают под словом \"run\". Если это проход по всем молекулам, то почему он содержал 2000 конфигураций, а не 1000. Также непонятно, какое число состояний было отброшено до момента, когда можно считать, что алгоритм пришел к равновесному состоянию."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Далее они пишут:\n",
"\n",
"> Runs near the transition required a 20x20x20 lattice and more than 8000 lattice configurations;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"На этот раз число конфигураций равно числу молекул, так что возможно в предыдущей части, правильное число 1000, а 2000 это опечатка. По-прежнему непонятно, сколько итераций нужно пропускать, чтобы алгоритм сошелся к нужному распределению."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Поэтому, нужно примерно посмотреть, как ведет себя алгоритм при разных температурах. Учтем, что согласно статье, точка фазового перехода находится в районе $\\beta=0.9$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Создадим начальную случайную конфигурацию:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lattice_initial = generate_random_lattice(10, 10, 10, random_state=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Промоделируем 30 проходов при нулевой обратной температуре. Должна наблюдаться произвольная ориентация молекул и энергия близкая к нулю."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energy0 = run_monte_carlo(lattice_initial, 0, n_passes=30)[1]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
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"execution_count": 11,
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1uQPhFhARUVqzVBsPBeZlbZoI2koZAAB4oxRS3vnhoDcVCSGnd9EO/aUkeNNR8GrMEwi3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\nNf4/fJs84cRnPOIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11bb6e8d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Видим некоторые случайные колебания энергии около 0."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Теперь рассмотрим значение обратной температуры 0.5."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"energy05 = run_monte_carlo(lattice_initial, 0.5, n_passes=30)[1]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120201c50>]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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DcjNSJUln9uhocE8AAADiG+E2Bgzu0UmS1K1TuyAtAQAAEAjhNgYcc2SaJMnBejIAAIBW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\npNMKH7NA4DAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11bded358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy05)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Видим, что требуется около трех проходов до того, как алгоритм придет в область конечного распределения."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Рассмотрим поведение вблизи точки фазового перехода (в изотропном состоянии)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energy085 = run_monte_carlo(lattice_initial, 0.85, n_passes=100)[1]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x120339128>]"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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RTQAAAIgohFsDUS0BAADAvwi3Bvj9BR0lSVf3bW9wSwAAACIL4dYATeNjJUkVVWaDWwIA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\nCi4VVWb9vK9Iz83apEqHYHpmG9cTfhzFx0Trih5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RlGT803dFYHv69Gls3boV9eqZX07K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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x120238a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy085)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Здесь примерно нужно 10 проходов."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Теперь рассмотрим температуру, соответствующие анизотропной фазе:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"При обратной температуре 1 сделаем 1000 проходов:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energy1 = run_monte_carlo(lattice_initial, 1, n_passes=1000)[1]"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x129b82ba8>]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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RGgAAoPoKNa+ZMuK6ePFiZWRkOEKrJPXv319JSUlaunRpwK9TUFAgi8WijIwMr22Ki4tV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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x121121630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Здесь видно, что скорее уже нужно где-то 100 проходов."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Теперь посмотрим при обратной температуре 2:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energy2 = run_monte_carlo(lattice_initial, 2, n_passes=1000)[1]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12c8f1080>]"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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JeGlw3Xe0wOZKAAAAQhPB1SQb9udIkvbnFNpcCQAAQGgiuJqke8sYu0sAAAAIaQRXkzRr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\nIiJihM8dj8LHbXqcBAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x129ca6630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Здесь требуется около 200 проходов. Флуктуации энергии достаточно небольшие."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"И теперь увеличим обратную температуру до 5."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energy5 = run_monte_carlo(lattice_initial, 5, n_passes=1000)[1]"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12f18a630>]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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TJK3aVWRzJQAAAJGJ4GqSnqnt7S4BAAAgohFcTdK4HBYAAACsQdoySeMcVwAAAFiD4GqS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\nBFcAAAA4AsEVAAAAjvD/Aa0oM+dUpe+vAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12c91a550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(energy5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Здесь кажется, что нужно около 800 проходов. Флуктуации еще меньше."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Общий вывод, что для перехода из случайного состояния в состояние, соответствующие изотропной фазе, требуется существенное число итераций. При этом флуктуации параметров в этой фазе существенно меньше.\n",
"\n",
"Для практической реализации имеет смысл действовать следующим образом: начать с обратной температуры равной 0 и отводить какое-то число итераций для выхода на режим и для подсчета средней энергии и параметра порядка, далее увеличивать обратную температуру на некоторое значение и продолжать из конечного состояния предыдущего этапа. Количества итераций нужно варьировать в зависимости от температуры. А именно, выглядит необходимым отводить большое число итераций для выхода на режим в области фазового перехода (чтобы система действительно успела перейти из изотропного состояния в анизотропное). Количество итераций для усреднения можно уменьшать с уменьшением температуры."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Построение зависимости средней энергии и параметра порядка от температуры"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Реализуем функцию, которая будет определять число итераций в зависимости от обратной температуры. Выбор этих чисел чисто эмпирический, из наблюдений предыдущего раздела и графиков зависимости параметров от температуры, которые получаются при их использовании."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_n_passes(beta_all):\n",
" n_transition = []\n",
" n_average = []\n",
" \n",
" for i, beta in enumerate(beta_all):\n",
" if beta <= 0.8:\n",
" n_transition.append(5)\n",
" n_average.append(100)\n",
" elif beta <= 1.1:\n",
" n_transition.append(int((beta - beta_all[i - 1]) * 2000))\n",
" n_average.append(100)\n",
" else:\n",
" n_transition.append(int((beta - beta_all[i - 1]) * 50))\n",
" n_average.append(max(1, int(100 / beta)))\n",
" \n",
" return n_transition, n_average"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Выберем интересующие значения обратной температуры, шаг варьируется в зависимости от области."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta_all = numpy.hstack([numpy.arange(0, 1.1, 0.05), \n",
" numpy.arange(1.1, 2, 0.1),\n",
" numpy.arange(2, 11, 1)])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0. , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35,\n",
" 0.4 , 0.45, 0.5 , 0.55, 0.6 , 0.65, 0.7 , 0.75,\n",
" 0.8 , 0.85, 0.9 , 0.95, 1. , 1.05, 1.1 , 1.2 ,\n",
" 1.3 , 1.4 , 1.5 , 1.6 , 1.7 , 1.8 , 1.9 , 2. ,\n",
" 3. , 4. , 5. , 6. , 7. , 8. , 9. , 10. ])"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"beta_all"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_transition_all, n_average_all = get_n_passes(beta_all)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_molecules = numpy.product(lattice_initial.shape[:-1])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Запустим описанный процесс с переходом от одной температуры к другой:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"lattice = lattice_initial\n",
"energy_all = []\n",
"order_all = []\n",
"\n",
"for beta, n_transition, n_average in zip(beta_all, n_transition_all, n_average_all): \n",
" lattice, energy, order_tensor = run_monte_carlo(lattice, beta,\n",
" n_passes=n_transition + n_average)\n",
" energy_all.append(energy)\n",
" order_all.append(order_tensor)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Вычислим средние значения энергии и параметра для каждой температуры:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"energy_mean = []\n",
"order_mean = []\n",
"for energy, order, n_transition, n_average in zip(energy_all, order_all, \n",
" n_transition_all, n_average_all):\n",
" order_to_average = order[-n_average * n_molecules:]\n",
" energy_to_average = energy[-n_average * n_molecules:]\n",
" energy_mean.append(numpy.mean(energy_to_average))\n",
" order_mean.append(compute_order_parameter_from_tensor(numpy.mean(order_to_average, axis=0))[0])\n",
"\n",
"energy_mean = numpy.asarray(energy_mean) \n",
"order_mean = numpy.asarray(order_mean)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Построим график средней энергии и параметра порядка в зависимости от обратной температуры:"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11ba918d0>"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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3jR49WpK0bds2DRo0SMeOHVNaWlqzh+L3ZxOJas/SVp6WXhqhZt2UZY2WkrrXmnHN9C0d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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11bcf4e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(beta_all, energy_mean, '.-', label=r'$\\langle E \\rangle$')\n",
"pyplot.plot(beta_all, order_mean, '.-', label=r'$\\eta$')\n",
"pyplot.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Видно резкое изменение значений в узком диапазоне температур. В идеале мы бы хотели увидеть нулевое значение параметра порядка до точки фазового перехода и полностью скачкообразные изменения энергии и параметра порядка в точке перехода. Учитывая приближенный характер моделирование, наверное, можно считать полученные графики удовлетворительными. Для улучшения качества зависимостей нужно использовать более длинные серии моделирования в области перехода (однако, возможно, нужно увеличить длину серий на порядки), а также можно попробовать использовать большее число частиц (например решетку 20x20x20, как указано в статье)."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Посмотрим теперь на точки в области фазового перехода и отметим точку $\\beta=0.89$ (точка фазового перехода, указанная в статье в виде $\\beta = 0.89 \\pm 0.05$):"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11b984e80>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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XvIiIiISEzqbZqi7xDbBNPbKdhdhB45p7YgePa+yJ7SDEdsQ2tN+F2iYBD7f/9V//xe23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\nAL9BuAUAAIDfINwCAADAb/x/4aBPJtKA0g4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11b97f978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pyplot.plot(beta_all, energy_mean, '.-', label=r'$\\langle E \\rangle$')\n",
"pyplot.plot(beta_all, order_mean, '.-', label=r'$\\eta$')\n",
"pyplot.xlabel(r\"$\\beta$\")\n",
"pyplot.xlim(0, 1.5)\n",
"pyplot.vlines(0.89, -1, 1, linestyles='dashed')\n",
"pyplot.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Видим, что эта точка вполне согласуется с нашими результатами."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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