Fin.

hands_on/HandsOn-16/HandsOn-16-Sol.ipynb

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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:eda61121733f1facb114934c5dd943d52ec00371f7920beabf140b38f69f79c2"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "import matplotlib as mpl; import matplotlib.pyplot as plt\n",
+      "%matplotlib inline\n",
+      "import os; import pickle"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Modelo de Potts Est\u00e1ndar orden 5"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def pottenergy(state1,state2):\n",
+      "    if (state1==state2):\n",
+      "        return -1.\n",
+      "    else:\n",
+      "        return 0.\n",
+      "def near_energy(nx,ny):\n",
+      "    global lattice\n",
+      "    global N\n",
+      "    return pottenergy(lattice[nx,ny],lattice[(nx-1)%N,ny])+\\\n",
+      "pottenergy(lattice[nx,ny],lattice[(nx+1)%N,ny]) + \\\n",
+      "pottenergy(lattice[nx,ny],lattice[nx,(ny+1)%N]) + \\\n",
+      "pottenergy(lattice[nx,ny],lattice[nx,(ny-1)%N])\n",
+      "def changeone():\n",
+      "    nx, ny = np.random.randint(0,N), np.random.randint(0,N)\n",
+      "    spin=lattice[nx,ny]\n",
+      "    if spin==-2:\n",
+      "        newspin=np.random.choice(np.array([-1,0,1,2]))\n",
+      "    elif spin==-1:\n",
+      "        newspin=np.random.choice(np.array([-2,0,1,2]))\n",
+      "    elif spin==0:\n",
+      "        newspin=np.random.choice(np.array([-2,-1,1,2]))\n",
+      "    elif spin==1:\n",
+      "        newspin=np.random.choice(np.array([-2,-1,0,2]))\n",
+      "    elif spin==2:\n",
+      "        newspin=np.random.choice(np.array([-2,-1,0,1]))\n",
+      "    en_i = near_energy(nx,ny)\n",
+      "    # Make the change\n",
+      "    lattice[nx,ny]=newspin\n",
+      "    # Calculate the new energy\n",
+      "    en_f = near_energy(nx,ny)\n",
+      "    if (en_f>en_i) and (np.random.random()>min(1,np.exp(-beta*(en_f-en_i)))):\n",
+      "        lattice[nx,ny]=spin # change it back\n",
+      "def magnetization():\n",
+      "    global lattice\n",
+      "    m=(float(N**2)-np.count_nonzero(lattice))/N**2\n",
+      "    return (5.*m-1.)/4"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "N=32\n",
+      "lattice=np.random.randint(-2,3,(N,N))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Animaci\u00f3n\n",
+      "%matplotlib osx\n",
+      "from matplotlib import animation\n",
+      "T=0.8\n",
+      "beta=1./T\n",
+      "fig=plt.figure(figsize=(10,10))\n",
+      "tplot=plt.imshow(lattice,cmap='gist_heat',vmin=-2.,vmax=2.,interpolation='None')\n",
+      "#plt.xlim(xmin+dx,xmax-dx)\n",
+      "#plt.ylim(ymin+dy,ymax-dy)\n",
+      "\n",
+      "def animate(i):\n",
+      "    global lattice\n",
+      "    global T\n",
+      "    for __ in range(100):\n",
+      "        changeone()\n",
+      "    tplot.set_array(lattice)\n",
+      "    return 0\n",
+      "    #plt.title(\"T=\"+str(T)+\" M=\"+str(round(magnetization()/N**2,3)))\n",
+      "\n",
+      "animacion = animation.FuncAnimation(fig, animate, np.arange(2,100000),interval=1, blit=False)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure(figsize=(10,10))\n",
+      "plt.imshow(lattice,cmap='gist_heat',vmin=-2.,vmax=2.,interpolation='None')\n",
+      "plt.savefig(\"/Users/juan/Documents/Trabajo/Andes/2015-V/MetodosComputacionales/hands_on/figures/potttiling.png\",dpi=100)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "N=32\n",
+      "#lattice=np.random.randint(-2,3,(N,N))\n",
+      "lattice=np.zeros((N,N))\n",
+      "numIter=1000*N**2\n",
+      "T=0.1\n",
+      "magnetizaciones=[]\n",
+      "for temp in np.linspace(0.6,1.1,15):\n",
+      "    print temp,\n",
+      "    T=temp\n",
+      "    beta=1./T\n",
+      "    mag=[]\n",
+      "    for i in range(numIter):\n",
+      "        changeone()\n",
+      "        if i>numIter-100:\n",
+      "            mag.append(magnetization())\n",
+      "    magnetizaciones.append([T,np.mean(mag)])\n",
+      "magnetizaciones=np.array(magnetizaciones)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure(figsize=(10,6))\n",
+      "plt.plot(magnetizaciones[:,0],magnetizaciones[:,1],\"o-\")\n",
+      "plt.axvline(1./np.log(1.+np.sqrt(5)), color='red')\n",
+      "plt.axhline(0, color='black')\n",
+      "plt.xlim(0.6,1.1)\n",
+      "plt.ylim(-0.1,1)\n",
+      "plt.title(\"Modelo de Potts q=5\\n Red de 32 X 32. Iteraciones en cada temperatura = 1e6 \")\n",
+      "plt.xlabel(\"T\")\n",
+      "plt.ylabel(\"r\")\n",
+      "plt.text(1.0,0.6,r\"$r=\\frac{5m-1}{4}$\",fontsize=20)\n",
+      "plt.text(0.995,0.55,u\"Par\u00e1metro de orden.\",fontsize=10)\n",
+      "#plt.savefig(\"/Users/juan/Documents/Trabajo/Andes/2015-V/MetodosComputacionalesLaboratorio/2015-V/actividades/talleres/Taller10/potts5.png\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}