Transfer-matrix approach to estimating coverage discontinuities and multicritical-point positions in two-dimensional lattice-gas phase diagrams

Abstract

We present a method of computing coverage discontinuities in two-dimensional lattice-gas phase diagrams using transfer matrices. By applying the method to Baxter’s generalized hard-square model, we find good agreement with exact results. This method also can be used to estimate the position of multicritical points, and we again find good agreement with exact results and with previous work on the Ising metamagnet. We discuss the transfer-matrix eigenvalue spectrum around an Ising tricritical point and verify the prediction of conformal invariance that the finite-size scaling behavior of each of the leading eigenvalues is governed by a different critical exponent at the critical point. We show numerically that the finite-size convergence of the free energy at the (Ising-like) tricritical point of Baxter’s model is consistent with a conformal anomaly of (7/10). We show that the justification of a commonly used method to locate multicritical points using simultaneous scaling of the correlation length and the "persistence length" is misleading. Finally we suggest a method of estimating the position of multicritical points using information from only one strip width.