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

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