Finite Size Effects and Pseudocritical Behavior. II: Potts Spin Model

Abstract

851Using the transfer matrices constructed by Kramers and Wannier's successive screw method for the 2-d (! x oo) and 3-d (l x m x oo) q state Potts model (2;?. q ;;;> 7), we examine the extent to which the presently available supercomputers can provide us with finite size effects and pseudocritical properties of the systems.We estimate the bulk coupling parameters Kc from the specific heat anomaly in two and three dimensions and also from the correlation length anomaly in two dimensions. In two dimensions, our results Kc are in good agreement with those given by the Potts duality formula. In three dimensions, however, we need extended precision computations to obtain the numerical results with sufficient accuracy.We regard the behavior of the exponent f.l., which characterizes the relation between the specific heat peak Cvo(l) and the lattice size l, as an indicator to discriminate the order of the phase transition by investigating Cvo(l) for several small values of l. § 1. IntroductionIn a previous work,1l referred to as I hereafter, we numerically investigated pseudocritical properties of the semi-infinite Ising spin and lattice gauge models in two and three dimensions using the transfer matrices constructed by Kramers and Wannier's successive screw method.2 lIn the present paper, the successive screw method is applied to the q-state Potts modePHl in two and three dimensions, as a generalization of the Ising model. We would like to examine the extent to which the available supercomputers can provide us with finite size effects and pseudocritical properties of the Potts model by means of the long-established transfer matrix method.A great number of numerical studies on the Potts model have been published. Among others, recent Monte Carlo studies 6 H 5 l have given significant results with a high degree of precision. The precision of our estimates in the present work in general is inferior to that of the latest Monte Carlo results. 13 H 5 l However, we hope that an extended precision computation will considerably improve the present results in the near future_ We show that the specific heat peak exponent f-t can be regarded as an indicator for discriminating the order of the phase transition, even though the lattice size is small.In § 2 the transfer matrices are constructed from the eigenvalue equations given by the successive screw method. In § § 3 and 4 the finite size effects are calculated in two and three dimensions, respectively_ The transition order of the Potts model is