The random chessboard model: A mean-field theory

Santiago D'Elía

Physica A: Statistical Mechanics and its Applications, 1986, vol. 137, issue 3, 603-622

Abstract: We consider here a mean-field theory of a new model spin Hamiltonian in d=2 dimensions that describes a system with two Ising-like variables per site that interact via a next-nearest neighbor (k2) and a four-spin (Г) coupling constants. The theory is formulated in terms of local averages of the order parameters. In terms of x=Гk2 we find second-order phase transitions for x⩽xc=118 and first-order phase transitions for x > xc. The critical curve corresponding to the uniform solution of the mean-field equations is calculated. We also study a particular nonuniform, periodic solution of the mean-field equations that describes an order characterized by the presence of domains and walls, and resembles a chessboard. We find that this chessboard solution is more stable than the uniform one for x≳xc and temperatures below the critical temperature. The existence of these instabilities of the uniform order near criticality could suggest that this model belongs to a new class of universality, a previously proposed idea.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:137:y:1986:i:3:p:603-622

DOI: 10.1016/0378-4371(86)90096-8

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