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Journal of Physics A Mathematical and General

Operator content of the multicritical magnetic hard-square model

D Kim, J-Y Choi, K Kwon

Published Sep 21, 1989• 0 citations
Publisher
DOI
10.1088/0305-4470/22/18/542

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Physics Letters A•May 1, 1979•0 citations
The commuting row-to-row transfer matrices of magnetic hard squares on the multicritical T manifold are shown to satisfy a special functional equation called an inversion identity.For strip widths up to N=32, these equations are solved numerically for the transfer matrix eigenvalues. The central charge or conformal anomaly c=1 is obtained from 1/N 2 corrections to the exact bulk free energy and scaling dimensions are obtained from the eigenvalue gaps. The magnetic scaling dimension is x m =1/8 and the sublattice density difference scaling dimension is x e =1/9(2-y), where y=2 lambda / pi and the interaction-dependent crossing parameter lambda varies between 0 and 2 pi /3. Scaling dimensions for further operators fall in the sequence x n =n 2 x e where n=1,2,3,4. The critical exponents also vary continuously along the multicritical line and are given by alpha =(14-9y)/(16-9y), beta m =9(2-y)/16(16-9y), beta e =1/2(16-9y), nu =9(2-y)/2(16-9y) and delta =15. These exponents are simply related to the exponents of the critical eight-vertex and Ashkin-Teller models, which also exhibit Z 2 *Z 2 symmetry, and the authors argue that these models lie in the same universality class.
The scaling behaviour of the magnetic hard-square lattice gas is examined in the vicinity of the multicritical line located by an exact solution. A simple scaling form is proposed for the singular part of the free energy and corresponding scaling forms are derived for the sublattice density difference, the magnetisation and the densities. These are all shown to be consistent with the exact results when restricted to the exact solution manifold. In the case of the densities this is achieved by proving appropriate elliptic function identities.