Eur. Phys. J. B (2012) 85: 170
https://doi.org/10.1140/epjb/e2012-20998-0

Regular Article

Equivalence between non-bilinear spin-S Ising model and Wajnflasz model

Departamento de Ciências Exatas, Universidade Federal de Lavras. CP 3037, 37200-000 Lavras, MG, Brazil

^a e-mail: ors@dex.ufla.br

Received: 7 December 2011
Received in final form: 10 March 2012
Published online: 28 May 2012

Abstract

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-S (for simplicity, we called as spin-S polynomial) onto spin-crossover state. The spin-S polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-S is given by 2(2^2S − 1). As an application of this mapping, we consider a general non-bilinear spin-S Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-S Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-S Ising model.