Stable, metastable and unstable solutions of a spin-1 Ising system obtained by the molecular-field approximation and the path probability method

Mustafa Keskin, Mehmet Ari and Paul H.E Meijer

Physica A: Statistical Mechanics and its Applications, 1989, vol. 157, issue 2, 1000-1017

Abstract: The spin-1 Ising model Hamiltonian with arbitrary bilinear (J) and biquadratic (K) pair interactions has been studied for zero field using the lowest approximation of the cluster variation method. The spin-1 or three-state system will undergo a first- or second-order phase transition depending on the ratio of the coupling parameters α = J/K. The critical temperatures and, in the case of the first-order phase transition, the limit of stability temperatures are obtained for different values of α calculating by the Hessian determinant. The first-order phase transition temperatures are found by using the free-energy values while increasing and decreasing the temperature. Besides the stable branches of the order parameters, we establish also the metastable and unstable parts of these curves.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:157:y:1989:i:2:p:1000-1017

DOI: 10.1016/0378-4371(89)90077-0

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