Rep:Mod:DMS3053-1

CMP Programming Experiment - Daniel Spencer, 00736964
Python IsingLattice.py script - Calculating the energy and magnetisation

   import numpy as np
   class IsingLattice:

       n_cycles = 0

       def __init__(self, n_rows, n_cols):
           self.n_rows = n_rows
           self.n_cols = n_cols
           self.lattice = np.random.choice([-1,1], size=(n_rows, n_cols))

       def energy(self):        # Returns the total energy of the current lattice configuration.
           J = 1.0 # Including this factor allows for potential modifications
           summed_spins = 0
           for i in range(len(self.lattice)): # Cycles through the rows of the spin array
               for j in range(len(self.lattice[i])): # Cycles through the elements in the 
               #ith row of the spin array
                   if i + 1 < self.n_rows and j + 1 < self.n_cols: # Multiplies i,jth element 
               #with i+1,j and i,j+1 and adds to sum (applies to elements with two 
               #neighbours in the array)
                       summed_spins += self.lattice[i,j] * self.lattice[i+1,j]
                       summed_spins += self.lattice[i,j] * self.lattice[i,j+1]
                   elif i + 1 == self.n_rows and j + 1 < self.n_cols: # Multiplies i,jth 
               #element with 0,j (due to periodic nature of the lattice) and i,j+1 
               #(applies to elements in final row)
                       summed_spins += self.lattice[i,j] * self.lattice[0,j]
                       summed_spins += self.lattice[i,j] * self.lattice[i,j+1]	
                   elif i + 1 < self.n_rows and j + 1 == self.n_cols: # Multiplies i,jth 
               #element with i+1,j and i,0 (applies elements in final column)
                       summed_spins += self.lattice[i,j] * self.lattice[i+1,j]
                       summed_spins += self.lattice[i,j] * self.lattice[i,0]
                   else: # Multiplied i,jth element with 0,j and i,0 (final array element - 
               #bottom right corner)
                       summed_spins += self.lattice[i,j] * self.lattice[0,j]
                       summed_spins += self.lattice[i,j] * self.lattice[i,0]
           energy = - J * summed_spins
           return energy

       def magnetisation(self):
           # Returns the total magnetisation of the current lattice configuration.
           magnetisation = 0
           for i in range(len(self.lattice)): # Cycles through the rows of the spin array
               for j in range(len(self.lattice[i])): # Cycles through the elements in the 
               #ith row of the spin array
                   magnetisation += self.lattice[i,j] # Updates the running total of the 
                   #magnetisation by adding i,jth value
           return magnetisation

       def montecarlostep(self, T):
           # complete this function so that it performs a single Monte Carlo step
           energy = self.energy()
           #the following two lines will select the coordinates of the random spin for you
           random_i = np.random.choice(range(0, self.n_rows))
           random_j = np.random.choice(range(0, self.n_cols))
           #the following line will choose a random number in the range [0,1) for you
           random_number = np.random.random()

       def statistics(self):
           # complete this function so that it calculates the correct values for the averages of E, E*E (E2), M, M*M (M2), and returns them
           return