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Quantum annealing with four-spin system
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Quantum annealing with four-spin system"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hamiltonian with the transverse field."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def flat_matrix(matrices):\n",
" result = None\n",
" for matrix in reversed(matrices):\n",
" if result is None:\n",
" result = matrix\n",
" continue\n",
" result = np.vstack(\n",
" (np.hstack((result * matrix[0][0], result * matrix[0][1])),\n",
" np.hstack((result * matrix[1][0], result * matrix[1][1])))\n",
" )\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sigma_z = np.array([[1.0, 0.0],\n",
" [0.0,-1.0]])\n",
"sigma_x = np.array([[0.0, 1.0],\n",
" [1.0, 0.0]])\n",
"I = np.eye(2)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def H(gamma, j):\n",
" h = 0.1\n",
" H = - j * (flat_matrix([sigma_z, sigma_z, I, I])\n",
" + flat_matrix([I, sigma_z, sigma_z, I])\n",
" + flat_matrix([I, I, sigma_z, sigma_z])\n",
" + flat_matrix([sigma_z, I, I, sigma_z]))\n",
" H += - h * (flat_matrix([sigma_z, I, I, I])\n",
" + flat_matrix([I, sigma_z, I, I])\n",
" + flat_matrix([I, I, sigma_z, I])\n",
" + flat_matrix([I, I, I, sigma_z]))\n",
" H += - gamma * (flat_matrix([sigma_x, I, I, I])\n",
" + flat_matrix([I, sigma_x, I, I])\n",
" + flat_matrix([I, I, sigma_x, I])\n",
" + flat_matrix([I, I, I, sigma_x]))\n",
" return H"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Time evolution of state in the Schroedinger picture."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def multi_spin(gamma, j):\n",
" dt = 0.001\n",
" state = np.array([[1.0+0.0j] for _ in range(2**4)])\n",
" state /= np.sqrt((np.absolute(state)**2).sum())\n",
"\n",
" result = []\n",
" t = dt\n",
" for _ in range(2000):\n",
" k1 = -1.0j * np.dot(H(gamma(t), j), state)\n",
" k2 = -1.0j * np.dot(H(gamma(t+0.5*dt), j), state + 0.5*dt*k1)\n",
" k3 = -1.0j * np.dot(H(gamma(t+0.5*dt), j), state + 0.5*dt*k2)\n",
" k4 = -1.0j * np.dot(H(gamma(t+dt), j), state + dt*k3)\n",
" state += (dt/6.0)*(k1+2*k2+2*k3+k4)\n",
" state /= np.sqrt((np.absolute(state)**2).sum())\n",
" result.append(np.copy(state))\n",
" t += dt\n",
" return result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualize the squared amplitudes."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"def show_result(result):\n",
" fig = plt.figure()\n",
" subplot = fig.add_subplot(111)\n",
" subplot.set_ylim(-0.1,1.1)\n",
" amps = [[] for _ in range(2**4)]\n",
" for state in result:\n",
" for c, spin in enumerate(state):\n",
" amps[c].append(np.absolute(spin[0])**2)\n",
"\n",
" for c in range(2**4):\n",
" subplot.plot(amps[c])\n",
" \n",
" amps = []\n",
" for c, spin in enumerate(result[-1]):\n",
" amps.append((c, np.absolute(spin[0])**2))\n",
" amps.sort(cmp=lambda x, y: cmp(y[1], x[1]))\n",
" return map(lambda (c, val): (format(c, '04b'), val) ,amps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Ferromagnetic system"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[('0000', 0.59461937576518642),\n",
" ('1111', 0.38020253617695265),\n",
" ('0010', 0.0029521438803220617),\n",
" ('0001', 0.0029521438803220531),\n",
" ('0100', 0.0029521438803220526),\n",
" ('1000', 0.0029521438803220487),\n",
" ('1011', 0.0027356887139028539),\n",
" ('0111', 0.0027356887139028448),\n",
" ('1101', 0.0027356887139028448),\n",
" ('1110', 0.0027356887139028357),\n",
" ('0011', 0.00059975830709321006),\n",
" ('1001', 0.00059975830709320692),\n",
" ('0110', 0.00059975830709320496),\n",
" ('1100', 0.00059975830709320388),\n",
" ('1010', 1.3862226294319509e-05),\n",
" ('0101', 1.3862226294318391e-05)]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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ChMhZdHe73Ta/9CXXfbF+PXz723DDDeq+OF/ZQpbd7btPW/jpePI4BsOq+lW8\neuGr+YtX/gUbmzbSFG+a6OqKyMtQkBAZYa1bPOquu+B733Ov3/EOdV+cr4H0ANuPbB9tbdhxZAep\nfIoyfxnr567ng2s/yMbmjWyYu4F4OD7R1RWRMVKQkBlveNgNlrzrLvjVr2DhQvirv4JbboHa2omu\n3dTTNtB2WmvDY52PYbHURerY1LyJ//Mb/4eNTRtZ07iGoKfmHZGpTkFCZqy9e13XxT33QCIB118P\n//f/wnXXafGoc1W0RfZ27T1tmenDA4cBWFKzhE1Nm/hf6/8XG5s3srh6saZhikxDChIyo2Sz8IMf\nuNaH//kfqK+Hj37UDZ5sbp7o2k1+qVyKR449Mtra8FDbQwxkBvD7/KxtXMvbl7+djU0b2di8kVnR\nWRNdXREZBwoSMiMcOgRf/arbvruz0y1d/U//BG9+swZPvpTuZPfoNMwH2x5k17Fd5Io5KkIVXNV0\nFX9w1R+wqXkT6+asIxKITHR1RWQCKEjItJXJwI9+5Lbtvv9+KC+Hm2+GD30Ili+f6NpNPiemYZ66\nfsO+nn0AzK2Yy9XNV/Pule9mU/MmXjHrFZqGKSJAiUHCGHM78AdAA/Ar4CPW2kde5N63AL8DrAZC\nwF7gk9ban5dUY5GX8dRTLjzcc4+bxrlxo5vK+fa3Q0T/aR516m6Y29q2se3wttFpmCvrV3Ltgmv5\ns1//MzY2bWRe5byJrq6ITFJjDhLGmBuBO4APADuBLcDPjDFLrLXdZ3nk14CfA38M9APvA35sjFln\nrf1VyTUXOUUy6aZsfvWrsG0b1NS41odbb4VLL53o2k0Ofak+Hmp7yIWGtm0v2A1T0zBFpBSltEhs\nAf7BWnsPgDHmQ8AbcAHh02febK3dcsalPzXGvAn4TVxrhkjJWltd68O3vw2Dg/DqV7uxD296E4RC\nE127iWOt5WD/QbYd3jY6FXPv8b0A1EfrtRumiFwwYwoSxpgAsBb4mxPXrLXWGHM/sOEcP4cByoHe\nsby3yAm9vW6RqK99zQWJ2bPdzIv3vQ8WLJjo2k2MfDHPno49o4s+bTu8jfbhdgCW1y1nY9NG/mjj\nH7GxaSMLqxZqGqaIXDBjbZGoBTyg84zrncDSc/wcfwhEge+O8b1lBsvn4ac/hW9+E+67z+2B8frX\nwyc/Ca97Hfhn2LDhwcwgDx95+LTVIhO5BCEvxBVzruA9l72HTc2b2DB3AzWRmomurohMY+P669cY\ncxPwCeAK5G1YAAAgAElEQVSNLzKe4jRbtmwhHj+9r3bz5s1s3rz5ItVQJpvHH4e773ZdF52dsGqV\nWzTqppvcGhAzgbWW5weeZ3vb9tHxDY91PkbRFqkpq2Fj80b+7Nf/jE3Nm1jbuJaQfwb36YjMMFu3\nbmXr1q2nXRsYGBjXOhhr7bnf7Lo2ksDbrLX3nXL9biBurX3LSzz7TuAfgRustT99mfdpAXbt2rWL\nlpaWc66fTA/d3W7J6rvvht273TLV73oXvPe9sHr1RNfu4kvn07S2t/JQ20NsP7Kd7W3bR7spFlUv\nYlPzJjY1bWJj80aW1ixVN4WInKa1tZW1a9cCrLXWtl7s9xtTi4S1NmeM2QVcC9wHo2MergU+/2LP\nGWM240LEjS8XImRmymbh3//dhYd//Vd37frr4c//3HVdTOdFo44MHmF723YXGo5sp7W9lWwhS5m/\njHVz1nHzZTezoWkDV869UqtFisikU0rXxmeBu0cCxYnpnxHgbgBjzKeA2dbam0de3zTysY8Cjxhj\nTjRIp6y1g+dVe5nSikU3VfPb33ZTN3t7Yc0auOMO2LwZ6uomuoYXXraQZU/HHra3beehIw+xvW07\nbYNtAMyvnM+GuRt418p3sWHuBlbVr9JsChGZ9MYcJKy13zXG1AJ/CdQDe4DXWGuPj9zSADSd8sj7\ncQM0vzhSTvgmbsqozDCPPebCw9at0NYGTU3w/ve7cQ+rVk107S6sjuGO01obHj32KOl8mpAX4vLZ\nl3PjihvZ0LSBDXM30FjeONHVFREZs5IGW1pr7wLuepGP3XLG62tKeQ+ZXg4dcsHh3nvhiSeguhre\n8Q4XHjZunB67beYKOR7venw0ODzU9hAH+w8CbonpDXM38KlrP8WGuRu0hbaITBszbNKcjKfubtdl\n8e1vuy6MsjK3SdanPuW26p7K4x6stRzqP8TOozvZcXQHO47uoLW9lXQ+TcAXoKWxhTctfdNoa0NT\nvOnlP6mIyBSkICEXVE+P26b7e9+DX/7SXbvuOvjWt9xqk7HYxNavVP3pfnYe3TkaHHYe3UlXoguA\nBZULWD93PTdcegPr566npbGFsD88wTUWERkfChJy3s4MD9bCr/86/P3fww03TL1Bk9lClsc6H2PH\nkR3sPLaTHUd2jO6CWRmuZN2cdXxw7QdZN2cd6+as00wKEZnRFCSkJN3d8MMfwne/C//xH6eHh7e+\ndeosFnViT4odR3aMtjS0treSKWQI+AJc1nAZr1r4Kv706j9l3Zx1LK5ZjM9MgwEdIiIXiIKEnLPj\nx+FHP3phePjCF+Atb5ka4aF9qJ1Hjz3qSvuj7Dy6k+6kW2T1kqpLWDdnHTeuuJH1c9ezumG1uihE\nRF6GgoS8pOeec+Hhhz90AyYBXvnKqREeuhJd7Dq2azQ0PHrsUY4NHQOgLlLH2tlrue3y21g/dz3r\n5qyjNlI7wTUWEZl6FCTkNNa6HTV/+EMXIB5/3G3Hfd118JWvwG/+JsyahEMCepI97GrfNdrasKt9\nF4cHDgNQXVbN2sa13HzZzVw++3Iun305TRVNWlpaROQCUJAQcjn4n/85GR7a2qCqyi1R/clPuhAx\nmWZb9Kf7aW1vPdlFcezR0fUaKkIVXD77ct654p2joWF+5XyFBhGRi0RBYobq6XHbcv/kJ26Pi/5+\nt8Lkm9/sytVXQ2ASrM7clehid/tudnfsZk/HHlrbW3mm9xkAooEoa2ev5S3L3jIaGi6pvkSDIUVE\nxpGCxAxhLfzqVy44/OQnsGOH2+tizRr4yEdceFizBibqP+4nFnja3bF7NDjs7tg9OqYhFoyxumE1\nr130Wj4x+xNcPvtyltQswfN5E1NhEREBFCSmtaEht67DT34C//ZvcOyY66J49avdeIfXvQ5mzx7/\neuWLeZ7ufvq0wLCnYw/96X4A6qP1rGlcw82X3cyahjWsaVzDwqqFamkQEZmEFCSmEWth7174xS9c\ncPjv/3bjH5YuhXe+E17/etdlMZ5LUw9nh3mi6wl2t7uwsLtjN493PU46nwZgYdVC1jSs4Q82/AFr\nGtewpmGNNq8SEZlCFCSmuI4OuP9++PnP3bG9HcJht77DHXe48HDJJRe/HkVb5Lne53i863Ee63xs\ntDzX9xwAnvFYXrecNY1ruGnlTaxpWMPqhtXEw/GLXzkREbloFCSmmGQSHnjAtTr8/OdueibA6tXw\n7ne7GRYbN7oNsi6W3lQvj3eeEhi6HuOJridI5pKAW6NhVf0q3rj0jayqX8XKWStZMWuFFncSEZmG\nFCQmuXwedu2C//xP1+Lw4IOQycCcOW6sw8c/Dq961cVZ2yFXyLGvZ99pLQyPdT7G0aGjAAS9ICvq\nVrCyfiXvWP4OVtWvYlX9Kupjk3iVKhERuaAUJCaZE8Hhv/7LlQcfhOFhiEZdd8Xf/q0LEJdeeuFm\nWGQLWZ7peYYnjz/J3uN7R4/7e/aTL+YBaI43s6p+Fe+57D2jgWFx9WIC3iSYIyoiIhNGQWKC5fNu\nJckTweGBB04Gh02b4E//1C1JvXbt+a/rcCIwnBoWnjz+5GmBYVZ0FsvrlnPN/Gu4/YrbWTlrJSvr\nV1IZrjzfL1VERKYhBYlxlkrBo4+6loYHHrg4wSGTz/Bs77PsPb6XvV17ebL7SfZ27eWZ3mdOCwwr\n6lZwzfxr+PAVH2bFrBUsr1uu/SZERGRMFCQusq4ut9nVibJrl5uSGYvBVVfBn/wJXHPN2IODtZau\nRBf7evbxdPfT7Ovex74eVw70HaBoi4Bbk2F53XKuXXAtH13/UZbXLVdgEBGRC0ZB4gIqFmHfPhcY\nHnzQHZ991n2sqcnNpnjXu1zLw8qV4J3DoownWhee7n56NCjs63bhYSAzAIDP+FhQuYBltct445I3\nsrR2Kctql7GibgU1kZqL+BWLiMhMpyBxHvr64JFH3HLTO3bA9u3Q2ws+H1x2Gbz2tS48bNzogsSL\nKdoix4aO8UzPM+zv2T8aGJ7ufppD/YdGWxcqw5Usq13GstplvGnpm1hWu4yltUu5pOoSQv7QOH3V\nIiIiJylInKNMxu1VsXOnCw07d8L+/e5jlZWwbp3bs2LjRrjySigvP/35QrFA22Abz/Y++4LyXN9z\noys9esZjYdVCltYu5S3L3sLSmqWjgaEuUqddLEVEZFJRkDgLa12XxInAsGMH7NkD2axbXnr1arfw\n0yc+AevXw6JFbipmrpDj+YHn2db5LM8+dXpYONB3gFwxB7iwsKBqAYuqF3HN/Gt4f8v7WVS9iEXV\ni1hQtYCgN45rWIuIiJyHGR8kikV47jk3BXPXLndsbXXdFgBLlrjWht/6LXdctiJDe+rQaED43DPP\n8OwOd36o/xAFWwAg4AuwsGohi6oX8dpFr2Vx9eLRsNAcb9b6CyIiMi3MqCCRz7vBkCfCQmsr7N7t\ndskEaG6GlrWW9//ucRqXHyAy5wBduQMc6DvA9/sO8OltBzjy70ewWADC/jCXVF3CoupFvHnZm0eD\nwqLqRTRVNGmLaxERmfamZZCw1m1m9cQTp5fHH3frOOBP07TyEPPXHOCa6w7grztAKnyAI4kD/KLv\nAD/MJWAvsBdqympYWLWQhVULuarpKhZUui6JxTWLmV0+W1tbi4jIjDblg0Rvr9s6ezQsPGF5/Nke\n+ottED9MoLaN6gWHKfu1NuqvP8yw/3m6s0dpA9qAoA0yPzufhdGFXN18NTdfdvNocFhQtYCKUMVE\nf4kiIiKT1pQJEsPD8OST0PpYih1Pt/HY84d5rvswAxyG+GFMpQsNhVe2UfiN1OhzxgsSrZhLc7yZ\npopLmBf/jdGgsLBqIbPLZ6sLQkREpESTOki87Y9vwsy2pEMp0uEkycgwmVAGyoFXuHui2RDluRDx\nfIjKXIB4bx3VxRDl+SAVhQCRXADwKJLC2v0U7H72GcNTRYO1hoLxKFpDEUOx6KNoPIzxGJ1kOTLd\n8tRJl2bk1ZlTMc1IN4fv9IunPX/ms8YYPJ+HweD5fHiehzE+PJ+H3+dhPHfued7Joz+Az+fD8/vx\n+/14noffH8DvD+Dze/j9QTy/hz8QxB8MEgwGCUUilEVilMXKKSuvIFpRQTReSSCo9SdERKR0kzpI\nHKrrgcACGFwCxxpgoBkG5o0cm2FwDolCiATQcdqTRaAA5EdKAWPcuTGFkeOpJYvPl8Xny40evRNH\nL4vny+P5snheHr+XxfPl8HunFF+egJfF7+UJ+E4cR677syMfzxHwsnheFr+Xw/NyeP4s/mASE0jj\nBdMQTFAsS1DwF8hayHCypIEEkChCIgdDBobz7jjog2KJQzV8RR9e0cNf8OMvevgL3ujRK3r4i76R\n1z78J+61J859o+cB6+4L4hG0HgH8BI2fgM8j4PMT9AKE/EGCgSDBQIhwKEw4VEaorIxoNEZZJEok\nVkGsspJYvJLyqmoqZ9VTXlWD55/Uf01FRGa0Sf0bev2xtxKsbCaDn2wgQK4mSKEyAYWnIPcUvmwB\nL1vAy4LJWkwWTMFA3mBzPkzB51oZij6K1lCwI+cYitZHoehzR+tRtB4F66dY8Cjk/RRtmJyNkbF+\nivgpWj/WBigSwI6cWwKjRwjC6PF8B2AWOBEhjMlgTBqfL3NKSeN5mdFS62UI+NP4vSx+L0vAyxL0\nMgRGz3MEfFlCfnce9GUJ+nIE/VmCvgzhQJqAlyEUSBEMpvAHkvgCSQqeJVOEZAFSFpLWMGwNCXwk\nMOQ8yHh5EoEiOV+BnFcg6+XJ+vPkvPzIeY6cP0/Wn8Uae/YvdXCkvIhAPkAoHySUCxLOBQjlXQnn\n/QTzfsIFP6Gin2DRTxg/IfyECBDyAoT9IcL+IGWhMsrCESJlUaLl5ZTHKymvqCJeV0v1rEaqGxqJ\n185SaBERGaNJ/Vvzrr/7IC0tLaOvi8Uix5IdPD14iGeGO3k2OciRbI72nKGjEKarWM4Apw+OjJKg\nzgzS4KVoDBRpDEBTKExTWQXzorOYH51NY6T+go6TSA7n6elIM9CXpb8ny3B/joH+LMmhPEP9OZKJ\nAonhHImhPMPDeZKJAulUgVSqQDKVJZPJk80XyOUKZPOQL0K+4IJQwfrIFz0KBT9FGyRnI6RtkCIB\nijboCkGsDWFtEEsICAFlJXwlOSCFMa74fCk8LzUSZFL4vRR+f5qA50rQyxD0MsS8DKGRMBPysoS8\nHCEvR9BfcEHGXyAUzBMKFggGCwTDlkCZJRy22KCfvA1QKPhIZzNk81myhRzZQo50MUfG5siQJ+M7\nWVL+HP3+FBkvTzqQI+PPkQnkSAcypAMZir7i6V9WBugaKc+evOwr+ohkyyjLhlzJBSnLBSjLuxIu\n+gkXA5SZAGUmSJkXIhIIEy2LEo3EiMUqiFdWUVk7i+qGRmbNbaaheQGhSKTEv0kiIpPfpA4SZ/L5\nfMyNzWZubDavepF7Erkkzw8f4WCinbZkL4fTwxzLZDmWszybDbItFaWbSop4wDCwnwBPUGsGmOVL\n0ujPMTtgmBsKMTdczrxIDfNiDcyLziXsD59TPSMxP5FFMV5ie41xl88X6e/OcvxYip6uDH1dGXqP\nZ9x5T4ahgRyDg3mGBnMMD6dIJlOk0y7QZPNFcgUfuaILMXkbIF8IUMgHyKRiJG2Igg1RtOHRYm0Y\nF17GGmDSQBKfL4HPJPF5STxfioAvid9LudDiyxDw0oR8rtUl5MsR9QpUBwqE/RAO+4hEglRURaiu\nq6K2vpzqujCVVXkCgR6yyR6GhwYZHhwgkRwmnU6RSCdJ5dKuFLOkbJaUyZHy8qS9HAOhNB3+LKlA\njnQgSzKYIRVMkw1kT6/+wEh57uSlUC40Gk4i2RDRbIhILkgkHyBSCBK1ASK+EBEvTCxQRixSTkV5\nnMqqampmNVA3Zy6NCxbRMG+BxrSIyKQzpYLEuYgGIiyvWsLyqiUvek++mOdIop2Dw0c5nOyhLTXA\n0Wyao9kiHXmPJ7NldA1XkiaMG2NxBDhCNf3M8g3R4GVpDFjmhgLMDUeZG65idlkVcyL11JfNIjgJ\nV630+33UNoSpbTi3MHShZNIFuo6kOHY4SdeRFN2daXqOpzh+rJfe7l4GBxIkEwlS6TzZXIFMzpAt\n+MgW/GSLQXKjJUyuECaRqyBfLKNYLKNQjFC0EayNAFHO/a/zSFgxCXy+FD6TwjMp/L40fpPG78sS\nMFn8vhwBX4GgzxL0G8qDfuojZVSUR4mVB6iuDRKvhHAoRVm4n1Coj1DwOIViD0PDgwwnh0lmkiRz\nadKFDKlilqTJkfRlSfpz9IVSHA0OkAhmSIbSJIMp0sHM6dU8PFK2g7GGSKaMaKbsZCDJBonkg0QL\nASI2SIQgUS9ENBAhGo5SWVFJVXUtsxrn0Dh/Ic1Ll1PdMPsCf5dFZCabdkHiXPh9fuaXNzG//MXb\nDIrFIj2ZXg4OH+Fwsovnk/0czSQ5ms3TnjM8mi7j35KndqW4jn7DPuIMU2US1HhparwCdX6oC/ip\nD4apD8VoDMdpLKtlTqSeqmAlPt/0XdQqFPZoWhSjaVHsor5PIZ9n32NPsn/PAdqeOcLx9n4Ge5MM\nDWRIpYqks5DO+Ujn/WQLfjLFIJlCkGwhTKYQIlcoI1cIky1ESBViDOUjFHMRCoUoxeJYw0oWSOA7\nEVZMGs+MhBSyBEyegM8S9EMoYKgLQSQM0aiPWNQQDKQJBhIEg4MEAgN4Xi/+8HEIdpOxSRKFDEmy\nJE2WhJcj6c/SHRl2gSSYIRFKkQylTo5JyQCHRsp/uTEnsXSEWKaMWCZMLBMimg8SzQeJESJmwsQC\nEcpDEeLlLojU1c+mYd485lyylIZ5CzSWRERG6bfBi/D5fNSV1VJXVsu6l7hvOJvgcOIoHeke2lN9\ndGSG6cym6MrmOZ63dBc8nssG6bVR+ikf6VIpAJ1AJwGyVDFEtS9JlS9HlVek2g/Vfj91gSC1wTLq\nQjFmhSuZFa6iPlxHRaB8WoePUnh+P8tblrO8ZfkF+Xz9vZ10HtlPT3srwz2HSfUfJTfcRaJ/gOHe\nPMPDhmTaI5X1k8iFSeZDJPNhErkykrkyUrkwqVyUVDZCJhMlm42RzUbJ5aKkc+UUClEK6SjFZAxr\no7iQci7jdJIYEhiS+EjjkcYzWfy4FpSgr0C1V6AxUCDo5Ql4GQL+DH4vTcCfxAsM4wWHMMFBbKQX\nGx0gW9HNQLSPjvggw6E0w+EUQ+EEBc/tG0MBODZStruxJOXpKLF0GdFMmFg2RCwXIpYPEi2GiJoQ\nMX+Y8lCMeHmcqsoaausbqG+ax9xFS5m9cJG6aESmEQWJ8xQLRlkeXMK5/PNVKBboTB3nWKqL9lQv\nHekBOjMJunIZunIF+vLQVfDYnw3SZyMMEiXHiZ1AEyPlCAGyxBmm0qSo8rJU+QpU+aHG71EbCFAT\nLGNWMMqscJzaUCW1oSpqQlWE/Prlfa4qq+uprK6HVVef1+dJJQbpOPos3ceeYeD4s6T6jpAd6qSY\n6oFsP6Y4hN8OY0iRzgVI5MIM58IM5aIM5csYypUxlI0ynCkjmYqSSMRIpaKk01HS6dhISImSy8bI\n5mIk8+UU8jEK2Qi2GMUS49zGqeSBBIaUa0khTYCMa0khi99k8Xyu28fvc8HE86fwBZKkQklSoSG6\nIkPkY/1kKrpJ1LSRDB8nHe0BUzg5uHWXCyLRTIRYumykVSRELBcklg8RLQZdi8hLBJG5i5aqRURk\nEtFP4zjyfB6zow3Mjjac0/3FYpHB3BAdqS660n0czwzQlRmmO5uiO5elJ5entwB9BR/Pp4P0F8MM\nEiU1+g9HhhMtHwBlJKkgRblJU+HLEfcVqPRb4p6hyu9R5Q9SGQhRE4hQE4pRHaqgNlRFXaiGiL9M\nrSAlKItWsGBJCwuWtLz8zS8hl83QfmQ/3Uf203/8eZJ9R8gO7aWQ7IZsH6YwhEcCv0nh92fwB3P4\nQwW8siI5PwzmI/TmYvRnowwORRkcjDE8HB0pMZLJKKlUlNRwOelUjHSqnEzGBZRcPkoqH6VQnEU+\nP9LVQwSIcW6/QlIYkiOtKCl8pMmbNEOkSfrS9Jo0ni+Nz5/G509iggkIJSA8COEENnyMYuRpCrFB\n8tEBcuV9BMJukG1FvuwFLSIxX4iYV0Z5OEY8Fqeqqoba+kYamuYxd8kyZi9YpCAicgHpp2kS8/l8\nVIbiVIbiLBvDc4lcks7UcTrT3XRnhujJDtObS9Gfy9CXz9GXKzBQgIGi4blsgMFikCEbPqMFpAD0\njZQDBMhSTpIKk6Lcl6Pc5Cn3isR8UOEZyj2PuN9PhT9I3B+iKlhGPBClMhijMlBBdShOPFiB36e/\ncqUIBEM0L1xJ88KV5/V5ctkMXceeo+voMwx0HSTRd5TMQDuF5IHTAolnUq5LJJjHH8rjCxfxlVmI\nWGwUihG37FsyGWRgIEp/f4zBwShDJ0JKX4zh/nISQxWkhmMkEhWk0jHSmRiZTIxsPkI2HyFfiJIp\n1lDIRSlky7BEsESBc5kyW6BjtJtnJKSYNN7I4NkT05Q9L+VCSuAgJrAXE0jhBVL4Axn8/hyBYIay\nQIZIKE15OEt1NE1VNEzFiSBSXUPtrEYa5i1g7uJlGiMicgb9NExD0UCEhYF5LKyYN+Znh7MJujO9\ndGf66MkM0JtN0JNN0pdL05fP0p8v0F+wDBdgoODjaM7PsA2QsCEShEme9g9AjpNhxCkjSZQ0MZMh\nanLEfHkqfEXKPYj5IOr5iHkeMc9PzB8k5gUo94epCISJemVUBKKUB6LEgzHigQp114xRIBhizvzl\nzJl/fmNJCvn8SCDZTyx3kMpMG5lsO4XicWywH19lJ55N4PmSbnXXQA4vlMcLF/FFXCAhAoUIZx0a\nks8bBgcj9HXEGD4eY7Cngv6eOEMDFQwOxhlOlJNIVpBIlZPKxMhko6RzUbL5MrL5MvLFCNl8FYVc\nmAJlFCkbaUWJ4haOezkjM3tOFONaUjxzFM/3HJ4vPdrV4/myBLwMfi9H0MsR9ucpCxaIRQvEy33U\n1QZpWlDO0ssaWXP1cuZecomCiEwrJf1tNsbcDvwB0AD8CviItfaRl7j/lcAdwArcZLa/ttZ+s5T3\nlosrFowSC0ZfckbLS8kX8wxkB+nNDNCfG6Q/O8xALkF/LsVALsNgPstgIc9gvsBQwTJYhKGCj86C\nx3AxQIoAKRsiRZAMZ05VTY2U7tErfnKUkSZCljKTJWLyRHx5ykyRqM8S9eGK5yPqeUR8HmU+PxF/\ngIjnJ+qFiHhBov4wUX+IqD9CxCujPBAh6o+qS+dFeH4/jc1LaWxeel6fp5DPc7zzebqO7KP32LMk\n+o6QHWwnn+zGZvuI5weptsN48Tb81c+OdNmMBJKyUwLJy41VLYAvBSYFyb4AvV1x+nrjDPTH6Ruo\nZHAozlCinKFEnESqnGS6nFQmQioXIZN14SRbDJMrlJEvxMnk608LKCdDysspwkgriiGFRwozMhbF\nI4vPZPGbHJ7J4Tc5/L4CQa9AKAChAETK/FRUhKiuKaeyOkS8KkhNXYiaWSHq55Qxe16UpsVRqmoV\nsGX8jDlIGGNuxIWCDwA7gS3Az4wxS6y13We5fz7wr8Bd8P/bu/dYy666gOPf3177dc6dufN+VKhY\nQVtNjJahPBQQLZEoEWM0NYNJ4yMaRGPsPzX+VcMfGjFafFWIRIxAm+Az/AFWaoygFggdMIClKhRK\nGWbazuM+zj1nP9b6+cfa994zd+6dx5k7c87M/D6TNWvvvdbdZ52zztnnd9Z+8VbgjcB7ReS4qn5s\n8qabWZQmKfvKvewr917xutrQslQvs9Assdgss9QMWGyGLLVDln3Fclux3DYs+4Zl7xn4wHJQBh5W\ngnDaO55tHENNWSFjpBkjciqK7uyZcXWXls5rR8GIkpqChlIaCvGU4umJp5BAP1FKgV4CvUToJQl9\nl5BLQi9xlC6lSBw9l1ImGT2XUbqc3loqu/kevbSg7/r00vKmuCutS1MOv+ilHH7RS69oPb5tOfX8\n1znxzJOcOfk0g1PPUC0cpx2dResFpF1CwoBUByRJxS5Xs2/fcdzhr+MKT1IEpFTorqMWeqD5RR40\nQDKKwQkjaBaFs2fmOX1qN2e7AGVhab4LUHYwGO1kMJpjpe4zqvvdCEq8PkobStpQ4ENJHXbhtSRQ\nopQoPZSSuLvnUoPaFrpgRahIGJFQ4ahIpMFRk0rbBSqhOxVZKTIoS6HfS+j1Evp9x9xcytzOlPn5\njPndGbv35ew5kLP/YMmBW3ocurXHvsMFaWoB981qkhGJ+4D3qOpfA4jI24A3A78AvHOT+r8CfEVV\n7+/mnxKR13brsUDCbClNUvaUu9lT7t7W9YYQqEPNoF1hqRmw0g5ZblcYtCNW/IhBWzPwFUPfMGgb\nhqFl4D3D4BmGwNArQ4VhgFEQFnzCSU0YqWOkKSPNqEhpyKjIxo47Gaes35Lt/OAF4mhLTkNOG3Np\nyfEU4sklUHQpF6UQKBJiLkKeQCYJRSJdHgObPHHkiaNYy1PyJO3yjNLFvHA5RZJTuLxbnlMkBWVa\nkCf5zAU5Lk05eMttHLzltm1b5/LiGZ47/n+cOfk1lk4/y8rZb1IvP087PI1WZ6GJwYnTlW5XR81c\n1jB/8Ju4W7+BKwJSKBQKBWgJWoBe4vXqpAGpQEYx90NYWixZOL2TxcWdLCzuYGGwg+XBHEsrOxgM\n51gezjGq+gzrPqOmR9WW1E0cUYmjKQVt6OF9yVDn8L4ktCWh6qEUKD1iwDLJRfViRCVUCDUJdZc3\nJDQ4addSmnjSJJAmgcwpWQp5quS5UOZCWQhl39HvOfp9R6+f0Oun7NiZMrczY8e8Y+eunN17c3bt\nzdm9r2DPgZyDL+5RlLP13rwZXFYgISIZcAT4ndVlqqoi8hjwmi3+7NXAYxuWPQo8eDmPbcx2SZKE\nMikp03JbRk4uJoRAFSpW2iHDLlgZ+aqbrhj5hqGvqULDMDSMfMMoeEa+pQoxgBmFQBU0JlUqhVEg\n3lNAAdYAAAvGSURBVCVWhcWQULcJlSZUmtKS0KijwdHiaEhpSGlJ0S1/1XrWbxh3YY6WjJa0yzM8\nmXgyPKkEcgKZBFIUJ0omikNJRckk7oXIBJzEPAVSEbKky0VI11JCJkm3LCFLuiSum3dkkpAmjqy7\n42ze3XU2S9JYrwuU4nRGmjhScThx3XRKmjicpGRJRiqOHfN72DF/F9xx1/a9GYgByukXnuXs819n\n+cwJBgvPUQ9O0QxO0Y4W0HoRbZYQv4KEIU660YSkwaUtB/pLHN51FpcFJFeSfD1YoYRQXsJoyiak\nJd74sIbRUsryQslgscfyUp/l5T6DlR6DQZ+VYY+VUY+VUZ/hqGRUl4zqHnVdUjWrgUtJ4wvatqT1\nBU0o8D5eSr8JBcHvILQ5gQLVIuarT+CSDrS9kJY4ulghNAgNdMGM0CI0JLQkeBKJuUvCWu4k4BIl\nTTTmTnEJOAcugTQVUgdZKqQpZJmQpgl5LmRZQp4n5EXMyzKhKBxl31H0HP05R9mLIzz9vmNuPqO/\nI2Xn7oy5+ZQd8xm79xfkZXJdjfBc7ojEfuI24OSG5SeBrXaWHt6i/ryIFKp68a2WMdexJEnoJT16\n6SQ3TtteIQRa9VRdMFP5mjo0VL6iCg1VF9BUoaEODSPfUoeWKqzmnno1aaAKgWYtV+qg1KrUCnWA\nVuMht16hVaFWYSXEzXmrgiehVaElodUEj9Di4s3p4qZ9LHd43Ca7pTZz6UHRVoRA0iW36bR204qT\nc+eTLnByaFc+nhPLREl2gtt5ACf7cUJXFgMsJ7EdDpCuLAEESAQSpMtXy+O8AHiPNDXUQ6QaIU1F\n0oyQZkTSVrh2hPN1TKEiDTWp1jjtQk5t4iXi97Tke1sOyoA0WSB1Hpe0pC7gnMelniQJiNMuj9Pi\nFFxAJhgcCAFGo4zBoGRpqcdoJWe4UjAc9KhXCkajnGpUMBqVVFVGXRXUdUFVFdR1TtPk1E1BUxc0\nbU7b5jRd8m1OG3K8z2h9gfc5IWS0ISOEgqAZIeQEn8UARzMgQ9V1d3lOu7R6p+erqSa+h1tW389C\n6HIPhJjL+PKAiEf1qavctnPZocPG3ESSJCEnIXcZO9k57eZMxAdPG1rqUNOElqYLepq1ZX5teaM+\n5sF30y2tetoQ8BpoVfEEfAi0GpNXxW/MUbxqrK9KOGeetXmvMWiK9bvNv8ZDLNfLIKyVSfz9rAk+\ndF8NGr8mNH4toN3fr84HBAVU16djLuu5dnUQQiFosV62Xi9ZX9fa9Gp50k1f2a/iGAJ6sm487JLy\npCXrN6T9lvTAetlqeQzm4npzPD18vMIrAxz+nPKLpYvVTTa8UhvztlLa2tHUjrZ21JWjbRxNndE0\nKVUV85jidF1n58w3TUbbxtz7dG26bVPaNiMEh/funHw1eZ+eM7+aRqNvcOLEFXXdZbncQOIF4vv/\n0Iblh4Ctmn1ii/qLFxuNuO+++9i1a9c5y44ePcrRo0cvucHGmBuLSxwucRTYmQlXWwgB7f754Ald\n0KXEQCxowKsnaKy3vizOA6gqQXVtPQBKQFVRXZ0HJdajm1Zdrz/+9+PrHa+z+vfdHWbW1jG+ztX/\nt34cznkM0LVla88FpR1bRjdWkbF+DVnvWzQEVD2+9QQf0FDH6eBjWduiocF7j6oneA8hEHyLAqKK\nEuIjhO6x1HfzQLfL5ol/+zyf/cQXWWsOSrJSbf2NfBVcViChqo2IPAHcDXwYQESkm//jLf7sceBH\nNyz7kW75BT344IO8/OVXdkVAY4wxkxk/9dkuJjej3nL+omPHjnHkyJFr1oRJxq3+EPglEblXRO4A\n3k08OuavAETkd0Vk/BoR7wa+XUR+T0RuF5G3Az/drccYY4wx17HLDjFV9UMish94B3EXxeeAN6nq\n812Vw8CtY/W/KiJvJp6l8evAs8AvqurGMzmMMcYYc52ZaKxKVR8iXmBqs7Kf32TZx4mnjRpjjDHm\nBnL9nKhqjDHGmJljgYQxxhhjJmaBhDHGGGMmZoGEMcYYYyZmgYQxxhhjJmaBhDHGGGMmZoGEMcYY\nYyZmgYQxxhhjJmaBhDHGGGMmZoGEMcYYYyZmgYQxxhhjJmaBhDHGGGMmZoGEMcYYYyZmgYQxxhhj\nJmaBhLkmHnnkkWk3wWwj688bi/WnuRIWSJhrwjZUNxbrzxuL9ae5EhZIGGOMMWZiFkgYY4wxZmIW\nSBhjjDFmYum0G7CFEuDJJ5+cdjvMNllYWODYsWPTbobZJtafNxbrzxvL2HdneS0eT1T1WjzOZRGR\ntwIfnHY7jDHGmOvYz6rqw1f7QWY1kNgHvAn4KjCabmuMMcaY60oJfBvwqKqeutoPNpOBhDHGGGOu\nD3awpTHGGGMmZoGEMcYYYyZmgYQxxhhjJmaBhDHGGGMmZoGEMcYYYyY2c4GEiPyqiDwtIkMR+aSI\n3DXtNpnzicgDIhI2pP/eUOcdInJcRFZE5GMi8rIN5YWI/JmIvCAiSyLytyJy8No+k5uTiLxORD4s\nIt/o+u4tm9S54v4TkT0i8kERWRCRMyLyXhGZu9rP72Zzsf4Ukfdt8nn9yIY61p8zQkR+S0Q+LSKL\nInJSRP5BRL5zk3oz8RmdqUBCRH4G+APgAeBO4L+AR0Vk/1QbZrbyBeAQcLhLr10tEJHfBH4N+GXg\nlcCA2Jf52N+/C3gz8FPA64FvAf7umrTczAGfA94OnHcO+Db238PAdwF3d3VfD7xnO5+IAS7Sn52P\ncu7n9eiGcuvP2fE64E+AVwFvBDLgn0Wkt1phpj6jqjozCfgk8Edj8wI8C9w/7bZZOq+vHgCOXaD8\nOHDf2Pw8MATuGZuvgJ8cq3M7EIBXTvv53Uype83fst39122cAnDnWJ03AS1weNrP+0ZNW/Tn+4C/\nv8DfWH/OcAL2d6/9a8eWzcxndGZGJEQkA44A/7K6TOOzegx4zbTaZS7oO7qh1C+LyAdE5FYAEbmN\n+ItnvC8XgU+x3pevIN7rZbzOU8AzWH9P1Tb236uBM6r62bHVP0b8xfyqq9V+s6U3dMPkXxKRh0Rk\n71jZEaw/Z9lu4ut8GmbvMzozgQQx4nLAyQ3LTxJfMDNbPgn8HDF6fRtwG/Dxbt/aYeIb8UJ9eQio\nuzf/VnXMdGxX/x0GnhsvVFVP3BhaH19bHwXuBX4YuB/4QeAjIiJd+WGsP2dS10fvAv5dVVePQ5up\nz+is3v3TzDhVfXRs9gsi8mnga8A9wJem0ypjzGZU9UNjs18Ukc8DXwbeAPzrVBplLtVDwHcDPzDt\nhmxllkYkXgA8MYoadwg4ce2bYy6Hqi4A/wO8jNhfwoX78gSQi8j8BeqY6diu/jsBbDxC3AF7sT6e\nKlV9mrjNXT3K3/pzBonInwI/BrxBVb85VjRTn9GZCSRUtQGeIB45CqwN6dwN/Oe02mUujYjsIG6U\njncbqROc25fzxH1uq335BPGAnvE6twPfCjx+jZptNrGN/fc4sFtE7hxb/d3EDeCnrlb7zcWJyIuB\nfcDql5P154zpgoifAH5IVZ8ZL5u5z+i0j0bdcGTqPcAKcV/eHcRTUE4BB6bdNkvn9dXvE08Tegnw\n/cDHiPve9nXl93d99+PA9wD/CPwvkI+t4yHgaeLw6hHgP4BPTPu53QyJeLrg9wLfRzxq+ze6+Vu3\ns/+AjwCfAe4iDs0+Bbx/2s//RksX6s+u7J3EL5mXdF8UnwGeBDLrz9lLXV+cIZ4GemgslWN1ZuYz\nOvUXbJMX8O3AV4mnsTwOvGLabbK0aT89Qjw1d0g8Cvhh4LYNdX6beIrSCvAo8LIN5QXxXOkXgCXg\nb4CD035uN0MiHmwXiLsTx9Nfbmf/EY82/wCw0G0Y/wLoT/v532jpQv0JlMA/EX/BjoCvAH/Ohh9o\n1p+zk7boSw/cu6HeTHxGpVuRMcYYY8xlm5ljJIwxxhhz/bFAwhhjjDETs0DCGGOMMROzQMIYY4wx\nE7NAwhhjjDETs0DCGGOMMROzQMIYY4wxE7NAwhhjjDETs0DCGGOMMROzQMIYY4wxE7NAwhhjjDET\n+38/DAt3Nc3NagAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x4e9bcd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"result = multi_spin(lambda t: 1.0/t, 1.0)\n",
"show_result(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Anti-ferromagnetic system"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[('1010', 0.48891305087437992),\n",
" ('0101', 0.48891305087437975),\n",
" ('1101', 0.0027802660012981369),\n",
" ('0111', 0.0027802660012981356),\n",
" ('1110', 0.0027802660012981239),\n",
" ('1011', 0.0027802660012981222),\n",
" ('0010', 0.0024100587336340776),\n",
" ('1000', 0.0024100587336340663),\n",
" ('0001', 0.0024100587336340659),\n",
" ('0100', 0.0024100587336340616),\n",
" ('0011', 0.00032800900495994487),\n",
" ('0110', 0.0003280090049599401),\n",
" ('1001', 0.00032800900495993696),\n",
" ('1100', 0.00032800900495993305),\n",
" ('1111', 6.6223174133947868e-05),\n",
" ('0000', 3.4340117537877319e-05)]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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FMgzy2sQEHxuc5z1jr+Gs/DUrXaaIyBlBQUJWvSBqc8fUNr43/Tg/rsAvo7XE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\nREJERERqUyIhIiIitf0fGl9AY9pI/58AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x4fb4090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"result = multi_spin(lambda t: 1.0/t, -1.0)\n",
"show_result(result)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.5"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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