Finite-size effect for the critical point of an anisotropic dimer model of domain walls

Bhattacharjee, Somendra M. ; Nagle, John F. (1985) Finite-size effect for the critical point of an anisotropic dimer model of domain walls Physical Review A, 31 (5). pp. 3199-3213. ISSN 1050-2947

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Official URL: http://pra.aps.org/abstract/PRA/v31/i5/p3199_1

Related URL: http://dx.doi.org/10.1103/PhysRevA.31.3199

Abstract

The finite-size effect is studied in the Kasteleyn model of dimers on the brick lattice. This model is isomorphic to an anisotropic domain-wall model. Asymptotic analysis of the exact Pfaffian solution for the specific heat establishes that finite-size-scaling theory is valid near the critical point of this model. The finite-size-scaling function is a function of a scaled temperature variable t and a shape factor scrr=N2/M, where 2N is the number of lattice points in the direction perpendicular to the preferred axis for the domain walls and 2M is the number of lattice points parallel to the preferred axis. The scaled temperature variable t is given by MN2t/(M+N2), where t is the reduced temperature. As a function of t the scaling function scrP(t,scrr) is a sequence of δ functions in the limit scrr=0 and a smooth single-peaked function in the limit scrr=∞. In the latter case the specific heat per lattice site can be written as & ∞), where α is the bulk specific-heat exponent with the known value of (½) and vM is found to have the value of 1. In the case scrr=0, the specific heat per lattice site can be written in an equivalent form by replacing M by N and vm by vN which takes the value vN=(½). According to finite-size-scaling theory vM and vN may be interpreted to be the critical exponents vy and vx, respectively, of the divergent length scales in the two principal directions. Our exact values of νm and νN are in agreement with the values of vy and vx predicted for general anisotropic domain-wall models.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:3104
Deposited On:09 Oct 2010 09:50
Last Modified:16 May 2016 13:58

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