RESHUFFLING SPINS WITH SHORT RANGE INTERACTIONS: WHEN SOCIOPHYSICS PRODUCES PHYSICAL RESULTS

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 ≈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)≈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≤p≤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 nonlinear 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.