{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 7-MonteCarlo Sampling" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/OpenJij/OpenJijTutorial/blob/master/source/en/007-MonteCarloSampling.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OpenJij implements Simulated Annealing (SA). If we keep tempereture constant, it is possible to sample spin sequences from the canonical distribution at this temperature.\n", "\n", "$$\n", "p(\\{\\sigma\\}) = \\frac{\\exp(-\\beta E(\\{\\sigma\\}))}{Z}, \\ Z = \\sum_{\\{\\sigma\\}}\\exp(-\\beta E(\\{\\sigma\\}))\n", "$$\n", "\n", "In the following, we deal with the fully-coupled ferromagnetic ising model.\n", "\n", "$$\n", "E(\\{\\sigma\\}) = \\frac{J}{N} \\sum_{i" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# visualize result\n", "plt.errorbar(temp_list, mag, yerr=mag_std)\n", "plt.plot(temp_list, mag)\n", "plt.xlabel('temperature', fontsize=15)\n", "plt.ylabel(r'|m|', fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This phenomenon, in which the value changes significantly from one temperature to another, is called a **phase transition**. In this model (when the system size is close to infinity), a phase transition occurs at a temperature of 1.0. It has been theoretically proven. \n", "However, it is often not possible to calculate the temperature at which the phase transition occurs theoretically in actual models. For this reason, MonteCarlo simulations are often used to study the properties of phase transitions numerically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binder cumulant\n", "\n", "Now, let us assume that we don't know the temperature of the phase transition, try to find the temperature of the phase transition as accurately as possible from the numerical simulations. \n", "Looking at the figure above, we can see the magnetization approach 0 as the temperature increases. However, it is not clear which temperature is the phase transition point. Phase transitions are theoretically phenomena that occurs in systems of infinite size, but simulations can only deal with finite size, which results in an error from the theory. This is called the **finite size effect**. Numerical analysis of system of infinite size is a seemingly impossible. However, in numerical simulation in statistical mechanics, the method of obtaining information of infinite system size from finite system size has been developed. The one of those methods it to use a quantity called **Binder cumulant**\n", "\n", "$$U_4 \\equiv \\frac{1}{2}\\left( 3- \\frac{\\langle m^4\\rangle}{\\langle m^2\\rangle^2} \\right)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# U_4\u306e\u8a08\u7b97\n", "def u_4(states):\n", " m = np.array([np.mean(state) for state in states])\n", " return 0.5 * (3-np.mean(m**4)/(np.mean(m**2)**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We defer to the statistical mechanics textbook for details. This quantity is close to 1 for ferromagnetism, where the magnetization approaches 1, and 0 for paramagnetism, where the magnetization approaches 0. Furthermore, the phase transition point is known to take a value independent of the system size. Therefore, we can perform the numerical experiments as described above for several system sizes and find that the point where the graph of $U_4$ intersects at a single point is the phase transition point. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# set a list of system size\n", "n_list = [40, 80, 120, 160]\n", "# set a list of temperature\n", "temp_list = np.linspace(0.5, 1.5, 30)\n", "\n", "# set sampler\n", "sampler = oj.SASampler(num_reads=300)\n", "\n", "u4_list_n = []\n", "for n in n_list:\n", " # make instance\n", " h, J = fully_connected(n)\n", " u4_temp = []\n", " for temp in temp_list:\n", " beta = 1.0/temp\n", " schedule = [[beta, 100 if temp < 0.9 else 300]]\n", " response = sampler.sample_ising(h, J, \n", " schedule=schedule, reinitialize_state=False,\n", " num_reads=100 if temp < 0.9 else 1000\n", " )\n", " u4_temp.append(u_4(response.states))\n", " u4_list_n.append(u4_temp)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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