This changes the Wordpress template hierarchy to use archive.php instead of home.php for the posts page if the front page settings are set to display a static page

functions.php

/**
 * Archive Template for Posts Page
 *
 * This changes the Wordpress template hierarchy to use archive.php for the posts page
 *
 * @author Chris Koelle
 *
 * @param  string $template
 * @return string
 */
function nh_posts_page_archive_template( $template ) {
	global $wp_query;

	if( $wp_query->is_posts_page && get_query_template( 'archive' ) !== '' )
		$template = get_query_template( 'archive' );
	return $template;
}
add_filter( 'template_include', 'nh_posts_page_archive_template' );