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

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