├── README.md ├── ILtimetrial.py ├── ILprofile.py ├── ILfinalframe.py ├── .gitignore ├── ILtemperaturerange.py ├── IsingLattice.py ├── ILanim.py ├── test_energy.py ├── ILcheck.py └── reference_data ├── 8x8.dat ├── 4x4.dat ├── 2x2.dat └── 16x16.dat /README.md: -------------------------------------------------------------------------------- 1 | # Ising-model 2 | 3 | These files form the basis of a 3rd year Monte-Carlo computational experiment to program and study the properties 4 | of a 2D Ising model. 5 | 6 | The files contain Python code templates that need to be completed and made functional. 7 | 8 | The experiment was originally developed by Niall Jackson. 9 | It was further developed by Aidan Chapman and Jonathan Hedley 10 | -------------------------------------------------------------------------------- /ILtimetrial.py: -------------------------------------------------------------------------------- 1 | import time #NB if running python < 3.3 use time.clock instead of time.process_time 2 | import IsingLattice as il 3 | 4 | 5 | #use a relatively big lattice of 25x25 so that we get more accurate timing data 6 | n_rows = 25 7 | n_cols = 25 8 | 9 | lattice = il.IsingLattice(n_rows, n_cols) 10 | #record the time at which we start running 11 | start_time = time.process_time() 12 | #do 2000 monte carlo steps 13 | for i in range(2000): 14 | lattice.montecarlostep(1.0) 15 | #record the time at which we stop running 16 | end_time = time.process_time() 17 | 18 | #work out how many seconds the loop took, and print it 19 | elapsed_time = end_time - start_time 20 | print("2000 steps took {} s".format(elapsed_time)) 21 | -------------------------------------------------------------------------------- /ILprofile.py: -------------------------------------------------------------------------------- 1 | import time # NB if running python < 3.3 use time.clock instead of time.process_time 2 | import cProfile 3 | import IsingLattice as il 4 | 5 | 6 | # use a relatively big lattice of 25x25 so that we get more accurate timing data 7 | n_rows = 25 8 | n_cols = 25 9 | save_profile = False 10 | 11 | lattice = il.IsingLattice(n_rows, n_cols) 12 | # record the time at which we start running 13 | start_time = time.process_time() 14 | # do 2000 monte carlo steps 15 | with cProfile.Profile() as prof: 16 | for i in range(2000): 17 | lattice.montecarlostep(1.0) 18 | # record the time at which we stop running 19 | end_time = time.process_time() 20 | 21 | # work out how many seconds the loop took, and print it 22 | elapsed_time = end_time - start_time 23 | print("2000 steps took {} s".format(elapsed_time)) 24 | 25 | prof.print_stats() 26 | 27 | # profiling data can be saved to a file and analysed with tools like pstats or SnakeViz 28 | if save_profile: 29 | prof.dump_stats("ising.prof") 30 | -------------------------------------------------------------------------------- /ILfinalframe.py: -------------------------------------------------------------------------------- 1 | from IsingLattice import IsingLattice 2 | from matplotlib import pyplot as plt 3 | import numpy as np 4 | 5 | n_rows = 8 6 | n_cols = 8 7 | temperature = 1.0 8 | runtime = 150000 9 | il = IsingLattice(n_rows, n_cols) 10 | spins = n_rows * n_cols 11 | times = range(runtime) 12 | E = [] 13 | M = [] 14 | for i in times: 15 | if i % 100 == 0: 16 | print("Step ", i) 17 | energy, magnetisation = il.montecarlostep(temperature) 18 | E.append(energy) 19 | M.append(magnetisation) 20 | fig = plt.figure() 21 | matax = fig.add_subplot(3, 1, 1) 22 | matax.matshow(il.lattice) 23 | enerax = fig.add_subplot(3, 1, 2) 24 | enerax.set_ylabel("Energy per spin") 25 | enerax.set_xlabel("Monte Carlo Steps") 26 | enerax.set_ylim([-2.1, 2.1]) 27 | magax = fig.add_subplot(3, 1, 3) 28 | magax.set_ylabel("Magnetisation per spin") 29 | magax.set_xlabel("Monte Carlo Steps") 30 | magax.set_ylim([-1.1, 1.1]) 31 | enerax.plot(times, np.array(E) / spins) 32 | magax.plot(times, np.array(M) / spins) 33 | plt.show() 34 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # Notebook Caches 6 | .ipynb_checkpoints/ 7 | 8 | # Folder for testing 9 | .no_commit/ 10 | 11 | # C extensions 12 | *.so 13 | 14 | # Distribution / packaging 15 | .Python 16 | env/ 17 | build/ 18 | develop-eggs/ 19 | dist/ 20 | downloads/ 21 | eggs/ 22 | lib/ 23 | lib64/ 24 | parts/ 25 | sdist/ 26 | var/ 27 | *.egg-info/ 28 | .installed.cfg 29 | *.egg 30 | 31 | # PyInstaller 32 | # Usually these files are written by a python script from a template 33 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 34 | *.manifest 35 | *.spec 36 | 37 | # Installer logs 38 | pip-log.txt 39 | pip-delete-this-directory.txt 40 | 41 | # Unit test / coverage reports 42 | htmlcov/ 43 | .tox/ 44 | .coverage 45 | .cache 46 | nosetests.xml 47 | coverage.xml 48 | 49 | # Translations 50 | *.mo 51 | *.pot 52 | 53 | # Django stuff: 54 | *.log 55 | 56 | # Sphinx documentation 57 | docs/_build/ 58 | 59 | # PyBuilder 60 | target/ 61 | 62 | #VIM 63 | *.swp 64 | -------------------------------------------------------------------------------- /ILtemperaturerange.py: -------------------------------------------------------------------------------- 1 | from IsingLattice import IsingLattice 2 | from matplotlib import pyplot as plt 3 | import numpy as np 4 | 5 | n_rows = 8 6 | n_cols = 8 7 | il = IsingLattice(n_rows, n_cols) 8 | il.lattice = np.ones((n_rows, n_cols)) 9 | 10 | # recalculate the energy after changing the lattice 11 | il.energy() 12 | il.magnetisation() 13 | 14 | spins = n_rows * n_cols 15 | runtime = 100000 16 | times = range(runtime) 17 | temps = np.arange(1.5, 3.5, 0.1) 18 | energies = [] 19 | magnetisations = [] 20 | energysq = [] 21 | magnetisationsq = [] 22 | for t in temps: 23 | for i in times: 24 | if i % 1000 == 0: 25 | print(t, i) 26 | energy, magnetisation = il.montecarlostep(t) 27 | aveE, aveE2, aveM, aveM2, n_steps = il.statistics() 28 | energies.append(aveE) 29 | energysq.append(aveE2) 30 | magnetisations.append(aveM) 31 | magnetisationsq.append(aveM2) 32 | # reset the IL object for the next cycle 33 | il.E_tally = 0.0 34 | il.E2_tally = 0.0 35 | il.M_tally = 0.0 36 | il.M2_tally = 0.0 37 | il.n_steps = 0 38 | fig = plt.figure() 39 | enerax = fig.add_subplot(2, 1, 1) 40 | enerax.set_ylabel("Energy per spin") 41 | enerax.set_xlabel("Temperature") 42 | enerax.set_ylim((-2.1, 0.1)) 43 | magax = fig.add_subplot(2, 1, 2) 44 | magax.set_ylabel("Magnetisation per spin") 45 | magax.set_xlabel("Temperature") 46 | magax.set_ylim((-1.1, 1.1)) 47 | enerax.plot(temps, np.array(energies) / spins) 48 | magax.plot(temps, np.array(magnetisations) / spins) 49 | plt.show() 50 | 51 | final_data = np.column_stack( 52 | (temps, energies, energysq, magnetisations, magnetisationsq) 53 | ) 54 | np.savetxt(f"{n_rows}x{n_cols}.dat", final_data) 55 | -------------------------------------------------------------------------------- /IsingLattice.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | 4 | class IsingLattice: 5 | def __init__(self, n_rows, n_cols): 6 | self.n_rows = n_rows 7 | self.n_cols = n_cols 8 | self.lattice = np.random.choice([-1, 1], size=(n_rows, n_cols)) 9 | 10 | current_en = self.energy() 11 | current_mag = self.magnetisation() 12 | 13 | # Running sums 14 | self.E_tally = current_en 15 | self.E2_tally = current_en**2 16 | self.M_tally = current_mag 17 | self.M2_tally = current_mag**2 18 | 19 | self.n_steps = 0 20 | 21 | def energy(self): 22 | """Return the total energy of the current lattice configuration.""" 23 | energy = 0.0 24 | return energy 25 | 26 | def magnetisation(self): 27 | """Return the total magnetisation of the current lattice configuration.""" 28 | magnetisation = 0.0 29 | return magnetisation 30 | 31 | def montecarlostep(self, temp): 32 | """A single Monte-Carlo trial move. Attempts to flip a random spin. 33 | Returns a tuple with the energy and magnetisation of the new configuration. 34 | """ 35 | # Complete this function so that it performs a single Monte Carlo step 36 | energy = self.energy() 37 | # The following two lines will select the coordinates of the random spin for you 38 | random_i = np.random.choice(range(0, self.n_rows)) 39 | random_j = np.random.choice(range(0, self.n_cols)) 40 | # The following line will choose for you a random number in the range [0,1) 41 | random_number = np.random.random() 42 | ... 43 | 44 | def statistics(self): 45 | """Returns the averaged values of energy, energy squared, magnetisation, 46 | magnetisation squared, and the current step, in this order.""" 47 | # Complete this function so that it calculates the correct values for the 48 | # averages of E, E*E (E2), M, M*M (M2), and returns them with Nsteps 49 | ... 50 | 51 | def delta_energy(self, i, j): 52 | """Return the change in energy if the spin at (i,j) were to be flipped.""" 53 | # Optional 54 | ... 55 | -------------------------------------------------------------------------------- /ILanim.py: -------------------------------------------------------------------------------- 1 | from IsingLattice import IsingLattice 2 | from matplotlib import pyplot as plt 3 | from matplotlib import animation 4 | import matplotlib as mpl 5 | 6 | n_rows, n_cols = 8, 8 7 | il = IsingLattice(n_rows, n_cols) 8 | spins = n_rows * n_cols 9 | temperature = 0.5 10 | 11 | figure = plt.figure() 12 | matax = figure.add_subplot(3, 1, 1) 13 | enerax = figure.add_subplot(3, 1, 2) 14 | enerax.set_ylabel("E per spin / k_B") 15 | magnetax = figure.add_subplot(3, 1, 3) 16 | magnetax.set_ylabel("M per spin") 17 | mat = matax.matshow(il.lattice, cmap=mpl.cm.gray, vmin=-1.0, vmax=1.0) 18 | matax.xaxis.set_ticks([]) 19 | matax.yaxis.set_ticks([]) 20 | 21 | (energies,) = enerax.plot([], [], "-", lw=2, label="E") 22 | enerax.legend() 23 | enerax.set_ylim(-2.1, 2.1) 24 | 25 | (magnetisations,) = magnetax.plot([], [], "-", lw=2, label="M") 26 | magnetax.legend() 27 | magnetax.set_ylim(-1.1, 1.1) 28 | 29 | xdata, ener_ydata, m_ydata = [], [], [] 30 | 31 | 32 | def data_gen(): 33 | global temperature 34 | t = data_gen.t 35 | spins = il.n_rows * il.n_cols 36 | while True: 37 | energy, magnetisation = il.montecarlostep(temperature) 38 | t += 1 39 | yield t, il.lattice, 1.0 * energy / spins, 1.0 * magnetisation / spins 40 | 41 | 42 | data_gen.t = 0 43 | 44 | 45 | def updateFigure(data): 46 | t, lattice, energy, m = data 47 | mat.set_data(lattice) 48 | xdata.append(t) 49 | ener_ydata.append(energy) 50 | m_ydata.append(m) 51 | xmin, xmax = enerax.get_xlim() 52 | if t >= xmax: 53 | enerax.set_xlim(xmin, 2 * xmax) 54 | enerax.figure.canvas.draw() 55 | magnetax.set_xlim(xmin, 2 * xmax) 56 | magnetax.figure.canvas.draw() 57 | enerax.set_title("Step {}.".format(t)) 58 | enerax.figure.canvas.draw() 59 | energies.set_data(xdata, ener_ydata) 60 | magnetax.figure.canvas.draw() 61 | magnetisations.set_data(xdata, m_ydata) 62 | 63 | return energies, mat 64 | 65 | 66 | anim = animation.FuncAnimation( 67 | figure, 68 | updateFigure, 69 | data_gen, 70 | repeat=False, 71 | interval=200, 72 | save_count=100, 73 | ) 74 | 75 | plt.show() 76 | 77 | E, E2, M, M2, N = il.statistics() 78 | 79 | print("Averaged quantities:") 80 | print("E = ", E / spins) 81 | print("E*E = ", E2 / spins / spins) 82 | print("M = ", M / spins) 83 | print("M*M = ", M2 / spins / spins) 84 | -------------------------------------------------------------------------------- /test_energy.py: -------------------------------------------------------------------------------- 1 | # This file contains test for different functionality of your IsingLattice program. 2 | # This is not meant for data analysis, only to check if your code is performing 3 | # tasks as expected. Test are run through the pytest framework installed by default 4 | # with Anaconda. 5 | 6 | from IsingLattice import IsingLattice 7 | 8 | import numpy as np 9 | 10 | 11 | def test_energy_all_up(): 12 | n = 10 13 | il = IsingLattice(n, n) 14 | il.lattice = np.ones((n, n)) 15 | 16 | assert il.energy() == -2 * n**2 17 | 18 | 19 | def test_energy_all_down(): 20 | n = 10 21 | il = IsingLattice(n, n) 22 | il.lattice = -np.ones((n, n)) 23 | 24 | assert il.energy() == -2 * n**2 25 | 26 | 27 | def test_mag_all_up(): 28 | n = 10 29 | il = IsingLattice(n, n) 30 | il.lattice = np.ones((n, n)) 31 | 32 | assert il.magnetisation() == n**2 33 | 34 | 35 | def test_mag_all_down(): 36 | n = 10 37 | il = IsingLattice(n, n) 38 | il.lattice = -np.ones((n, n)) 39 | 40 | assert il.magnetisation() == -(n**2) 41 | 42 | 43 | def test_delta_energy(): 44 | n = 10 45 | il = IsingLattice(n, n) 46 | 47 | rand_i = np.random.choice(range(0, n)) 48 | rand_j = np.random.choice(range(0, n)) 49 | 50 | deltaE = il.delta_energy(rand_i, rand_j) 51 | 52 | en0 = il.energy() 53 | il.lattice[rand_i, rand_j] *= -1 54 | en1 = il.energy() 55 | 56 | assert en1 - en0 == deltaE 57 | 58 | 59 | def test_delta_mag(): 60 | n = 10 61 | il = IsingLattice(n, n) 62 | 63 | rand_i = np.random.choice(range(0, n)) 64 | rand_j = np.random.choice(range(0, n)) 65 | 66 | deltaM = -2 * il.lattice[rand_i, rand_j] 67 | 68 | mn0 = il.magnetisation() 69 | il.lattice[rand_i, rand_j] *= -1 70 | mn1 = il.magnetisation() 71 | 72 | assert mn1 - mn0 == deltaM 73 | 74 | 75 | def test_random(): 76 | """ 77 | Creates a random lattice by flipping n*n random spins and 78 | tracking the changes in energy. 79 | """ 80 | 81 | n = 10 82 | il = IsingLattice(n, n) 83 | il.lattice = np.ones((n, n)) 84 | en = il.energy() 85 | 86 | for _ in range(n**2): 87 | rand_i = np.random.choice(range(0, n)) 88 | rand_j = np.random.choice(range(0, n)) 89 | 90 | en += delta_energy(il, rand_i, rand_j) 91 | 92 | il.lattice[rand_i, rand_j] *= -1 93 | 94 | print(en, il.energy()) 95 | assert en == il.energy() 96 | 97 | 98 | def delta_energy(il, i, j): 99 | "Return the change in energy if the spin at (i,j) is flipped." 100 | return ( 101 | 2 102 | * il.J 103 | * il.lattice[i, j] 104 | * ( 105 | il.lattice[i, (j - 1) % il.n_cols] 106 | + il.lattice[i, (j + 1) % il.n_cols] 107 | + il.lattice[(i - 1) % il.n_rows, j] 108 | + il.lattice[(i + 1) % il.n_rows, j] 109 | ) 110 | ) 111 | return delta_energy 112 | -------------------------------------------------------------------------------- /ILcheck.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | import IsingLattice as il 4 | 5 | 6 | #first do some setting up of the plots 7 | #we want a plot with 3 columns, one for each case 8 | 9 | lattice_size = 4 10 | 11 | fig = plt.figure() 12 | left_figure = fig.add_subplot(1,3,1) 13 | middle_figure = fig.add_subplot(1,3,2) 14 | right_figure = fig.add_subplot(1,3,3) 15 | 16 | #plot the low energy state in the left figure 17 | lattice = il.IsingLattice(lattice_size, lattice_size) 18 | lattice.lattice = np.ones((lattice_size,lattice_size)) 19 | left_figure.matshow(lattice.lattice) 20 | left_figure.set_title("Energy Minimum") 21 | left_figure.xaxis.set_ticks([]) 22 | left_figure.yaxis.set_ticks([]) 23 | 24 | target_energy = -2.0*lattice_size*lattice_size 25 | actual_energy = lattice.energy() 26 | target_magnetisation = 1.0*lattice_size*lattice_size 27 | actual_magnetisation = lattice.magnetisation() 28 | left_figure.text(0, 4, "Expected E = {}".format(target_energy)) 29 | left_figure.text(0, 4.4, "Actual E = {}".format(actual_energy)) 30 | left_figure.text(0, 4.8, "Expected M = {}".format(target_magnetisation)) 31 | left_figure.text(0, 5.2, "Actual M = {}".format(actual_magnetisation)) 32 | 33 | #plot the "perfectly disordered", high energy, state in the right figure 34 | high_energy_latticerow1 = [1, -1]*int(lattice_size/2) 35 | high_energy_latticerow2 = [-1, 1]*int(lattice_size/2) 36 | lattice.lattice = np.array([high_energy_latticerow1, high_energy_latticerow2]*int(lattice_size/2)) 37 | right_figure.matshow(lattice.lattice) 38 | right_figure.set_title("Energy Maximum") 39 | right_figure.xaxis.set_ticks([]) 40 | right_figure.yaxis.set_ticks([]) 41 | target_energy = 2.0*lattice_size*lattice_size 42 | actual_energy = lattice.energy() 43 | target_magnetisation = 0.0 44 | actual_magnetisation = lattice.magnetisation() 45 | right_figure.text(0, 4, "Expected E = {}".format(target_energy)) 46 | right_figure.text(0, 4.4, "Actual E = {}".format(actual_energy)) 47 | right_figure.text(0, 4.8, "Expected M = {}".format(target_magnetisation)) 48 | right_figure.text(0, 5.2, "Actual M = {}".format(actual_magnetisation)) 49 | 50 | #plot a random configuration in the middle figure 51 | lattice.lattice = np.random.choice([1,-1], (lattice_size,lattice_size)) 52 | #lattice.lattice = np.ones((lattice_size, lattice_size)) 53 | middle_figure.matshow(lattice.lattice) 54 | middle_figure.set_title("Random Configuration") 55 | middle_figure.xaxis.set_ticks([]) 56 | middle_figure.yaxis.set_ticks([]) 57 | target_energy = -1.0*np.sum(np.multiply(lattice.lattice, np.roll(lattice.lattice, 1, 0))) 58 | target_energy -= 1.0*np.sum(np.multiply(lattice.lattice, np.roll(lattice.lattice, 1, 1))) 59 | actual_energy = lattice.energy() 60 | target_magnetisation = 1.0*np.sum(lattice.lattice) 61 | actual_magnetisation = lattice.magnetisation() 62 | middle_figure.text(0, 4, "Expected E = {}".format(target_energy)) 63 | middle_figure.text(0, 4.4, "Actual E = {}".format(actual_energy)) 64 | middle_figure.text(0, 4.8, "Expected M = {}".format(target_magnetisation)) 65 | middle_figure.text(0, 5.2, "Actual M = {}".format(actual_magnetisation)) 66 | 67 | #draw the whole figure on the screen 68 | plt.show() 69 | -------------------------------------------------------------------------------- /reference_data/8x8.dat: -------------------------------------------------------------------------------- 1 | 5.000000000000000000e-01 -2.000000000000000000e+00 4.000000000000000000e+00 9.999984374999999481e-01 1.000000000000000000e+00 0.000000000000000000e+00 2 | 5.200000000000000178e-01 -2.000000000000000000e+00 4.000000000000000000e+00 9.999984374999999481e-01 1.000000000000000000e+00 0.000000000000000000e+00 3 | 5.400000000000000355e-01 -1.999968750000000073e+00 3.999902343750000089e+00 9.999937500000000146e-01 9.999877929687499556e-01 6.001157407387869985e-03 4 | 5.600000000000000533e-01 -2.000000000000000000e+00 3.999975585937499911e+00 9.999984374999999481e-01 9.999975585937499467e-01 -4.982461734712002703e-03 5 | 5.799999999999999600e-01 -1.999984374999999925e+00 3.999926757812500178e+00 9.999953124999999554e-01 9.999926757812499512e-01 -2.043744426203393440e-03 6 | 5.999999999999999778e-01 -2.000000000000000000e+00 3.999975585937499911e+00 9.999984374999999481e-01 9.999975585937499467e-01 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