Reshuffling spins with short range interactions: When sociophysics produces physical results

TL;DR

This study investigates the effects of Galam reshuffling in opinion dynamics modeled by the nearest neighbor Ising model, revealing non-linear changes in critical temperature and exponents with reshuffling probability, contrasting with classical and mean-field results.

Contribution

It provides a detailed numerical analysis of Galam reshuffling effects on the Ising model, highlighting deviations from classical and mean-field critical behaviors.

Findings

Critical temperature varies non-linearly with reshuffling probability p.

Reshuffling leads to critical exponents differing from classical and mean-field values.

Galam p=1 result is reproduced by a Solomon network realization.

Abstract

Galam reshuffling introduced in opinion dynamics models is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature T_C \approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different from both values, not reshuffled (T_C=2/arcsinh(1) \approx 2.27 [J/k_B]) and mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as function of 0 \leq p \leq 1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of T_C as function of p is obtained and exhibits a non-linear behavior. The simplest Solomon network realization is noted to reproduce Galam p=1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean-field values.