Edge phase transitions of the tricritical Potts model in two dimensions

Abstract

Using Monte Carlo techniques and finite-size analysis, we investigate several two-dimensional lattice models with open edges, including the Blume-Capel model and the q=1 and 3 Potts models with vacancies. At bulk tricriticality, we find that the open edges are dominated by the vacancies when the surface coupling K(s) and the chemical potential D(s) of the vacancies assume the bulk values. When K(s) and/or D(s) is sufficiently enhanced, an edge phase transition takes place, beyond which spontaneous one-dimensional order occurs on the edges. Edge phase transitions can also be induced by a surface magnetic field H(s) . We numerically determine a number of edge critical exponents and derive phase diagrams in terms of K(s) , D(s) , and H(s) . In the low-temperature region, we observe first-order transitions when K(s) and D(s) are varied; the associated hysteresis loops of surface quantities are remarkably asymmetric. Some further insight into these edge transitions is provided by the exact equivalence of the tricritical q=1 Potts model and the Ising model.