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

A. O. Sousa·K. Malarz·S. Galam
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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.

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A. O. Sousa, K. Malarz, S. Galam. 2005-03-30. Reshuffling spins with short range interactions: When sociophysics produces physical results. https://doi.org/10.1142/s0129183105008102

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