Edge phase transitions of the tricritical Potts model in two dimensions

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.