An Ising model having permutation spin motivated by a permutation complexity measure

Mark Dukes

Physica A: Statistical Mechanics and its Applications, 2023, vol. 626, issue C

Abstract: In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin, a permutation, to the other. This model is motivated by a complexity measure for declarative systems. For such systems a state is a permutation and the permutation sorting complexity measures the average sequential disorder of neighbouring states. To measure the relative disorder between two spins we use a symmetrized version of the descent permutation statistic that has appeared in the works of Chatterjee & Diaconis and Petersen. The classical Ising model corresponds to the length-2 permutation case of this new model. We consider and prove some elementary properties for the 1D case of this model in which spins are length-3 permutations.

Keywords: Ising model; Permutation entropy; Permutation complexity; Declarative process; Permutation spin; Combinatorial physics (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006453

DOI: 10.1016/j.physa.2023.129090

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