Bhattacharjee, Somendra M. ; Nagle, John F. (1985) Finitesize effect for the critical point of an anisotropic dimer model of domain walls Physical Review A, 31 (5). pp. 31993213. ISSN 10502947

PDF
 Publisher Version
1MB 
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 finitesize effect is studied in the Kasteleyn model of dimers on the brick lattice. This model is isomorphic to an anisotropic domainwall model. Asymptotic analysis of the exact Pfaffian solution for the specific heat establishes that finitesizescaling theory is valid near the critical point of this model. The finitesizescaling function is a function of a scaled temperature variable t and a shape factor scrr=N^{2}/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 MN^{2}t/(M+N^{2}), 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 singlepeaked function in the limit scrr=∞. In the latter case the specific heat per lattice site can be written as & ∞), where α is the bulk specificheat exponent with the known value of (½) and v_{M} 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 v_{m} by v_{N} which takes the value v_{N}=(½). According to finitesizescaling theory v_{M} and v_{N} may be interpreted to be the critical exponents v_{y} and v_{x}, respectively, of the divergent length scales in the two principal directions. Our exact values of ν_{m} and ν_{N} are in agreement with the values of v_{y} and v_{x} predicted for general anisotropic domainwall 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 
Repository Staff Only: item control page