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

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 Tc approximate to 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) approximate to 2.27 [J/k(B)]) and mean-field (TC = 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 TC as function of p is obtained and exhibits a nonlinear behavior. The simplest Solomon network realization is noted to reproduce Calam 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.