SSEP coupling.py

From Werner KRAUTH

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import math
import random
Ntrials = 100

for NPart in [8, 16, 32, 64]:
    NSites = 2 * NPart
    Coupling  = []
    for Iter in range(Ntrials):
        ConfLow = {-1: -1, NPart: NSites}; ConfHigh = {-1: -1, NPart: NSites}
        for k in range(NPart):
            ConfLow[k] = k
            ConfHigh[NPart - 1 - k] = NSites - 1 - k
        iter = 0
        while True:
            iter += 1
            Active = random.randint (0, NPart - 1)
            sigma = random.choice([-1, 1])
            if ConfLow[Active + sigma] != ConfLow[Active] + sigma: ConfLow[Active] += sigma
            if ConfHigh[Active + sigma] != ConfHigh[Active] + sigma: ConfHigh[Active] += sigma
            CLow = [ConfLow[k] for k in range(NPart)]
            CHigh = [ConfHigh[k] for k in range(NPart)]
            for k in range(NPart):
                if CLow[k]> CHigh[k]: print(Error)
            if ConfLow == ConfHigh:
                Coupling.append(iter / NPart ** 3 / math.log(NPart))
                break
    print(NPart, sum(Coupling) / len(Coupling))

 N t_coup / N^3 / log N
 8 1.2698
16 1.1993
32 1.1190
64 1.1028