09: Copy example code before adaption

Exercise sheet 9/latticescalar.py

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+import numpy as np
+rng = np.random.default_rng()  
+import matplotlib.pylab as plt
+%matplotlib inline
+
+def potential_v(x,lamb):
+    '''Compute the potential function V(x).'''
+    return lamb*(x*x-1)*(x*x-1)+x*x
+
+def neighbor_sum(phi,s):
+    '''Compute the sum of the state phi on all 8 neighbors of the site s.'''
+    w = len(phi)
+    return (phi[(s[0]+1)%w,s[1],s[2],s[3]] + phi[(s[0]-1)%w,s[1],s[2],s[3]] +
+            phi[s[0],(s[1]+1)%w,s[2],s[3]] + phi[s[0],(s[1]-1)%w,s[2],s[3]] +
+            phi[s[0],s[1],(s[2]+1)%w,s[3]] + phi[s[0],s[1],(s[2]-1)%w,s[3]] +
+            phi[s[0],s[1],s[2],(s[3]+1)%w] + phi[s[0],s[1],s[2],(s[3]-1)%w] )
+
+def scalar_action_diff(phi,site,newphi,lamb,kappa):
+    '''Compute the change in the action when phi[site] is changed to newphi.'''
+    return (2 * kappa * neighbor_sum(phi,site) * (phi[site] - newphi) +
+            potential_v(newphi,lamb) - potential_v(phi[site],lamb) )
+
+def scalar_MH_step(phi,lamb,kappa,delta):
+    '''Perform Metropolis-Hastings update on state phi with range delta.'''
+    site = tuple(rng.integers(0,len(phi),4))
+    newphi = phi[site] + rng.uniform(-delta,delta)
+    deltaS = scalar_action_diff(phi,site,newphi,lamb,kappa)
+    if deltaS < 0 or rng.uniform() < np.exp(-deltaS):
+        phi[site] = newphi
+        return True
+    return False
+
+def run_scalar_MH(phi,lamb,kappa,delta,n):
+    '''Perform n Metropolis-Hastings updates on state phi and return number of accepted transtions.'''
+    total_accept = 0
+    for _ in range(n):
+        total_accept += scalar_MH_step(phi,lamb,kappa,delta)
+    return total_accept
+
+def batch_estimate(data,observable,k):
+    '''Devide data into k batches and apply the function observable to each.
+    Returns the mean and standard error.'''
+    batches = np.reshape(data,(k,-1))
+    values = np.apply_along_axis(observable, 1, batches)
+    return np.mean(values), np.std(values)/np.sqrt(k-1)
+
+lamb = 1.5
+kappas = np.linspace(0.08,0.18,11)
+width = 3
+num_sites = width**4
+delta = 1.5  # chosen to have ~ 50% acceptance
+equil_sweeps = 1000
+measure_sweeps = 2
+measurements = 2000
+
+mean_magn = []
+for kappa in kappas:
+    phi_state = np.zeros((width,width,width,width))
+    run_scalar_MH(phi_state,lamb,kappa,delta,equil_sweeps * num_sites)
+    magnetizations = np.empty(measurements)
+    for i in range(measurements):
+        run_scalar_MH(phi_state,lamb,kappa,delta,measure_sweeps * num_sites)
+        magnetizations[i] = np.mean(phi_state)
+    mean, err = batch_estimate(np.abs(magnetizations),lambda x:np.mean(x),10)
+    mean_magn.append([mean,err])
+
+plt.errorbar(kappas,[m[0] for m in mean_magn],yerr=[m[1] for m in mean_magn],fmt='-o')
+plt.xlabel(r"$\kappa$")
+plt.ylabel(r"$|m|$")
+plt.title(r"Absolute field average on $3^4$ lattice, $\lambda = 1.5$")
+plt.show()