Roughening transition in mean-field and pair approximation of Ising models

Abstract

It is shown that the macroscopic phenomena of the roughening transition in an Ising interface model can be connected with a property, corresponding to a second-order phase transition, of the local thermodynamic potential for interfaces with an even symmetry. Using this connection a method is developed to evaluate the roughening temperature in first- and second-order mean-field approximations of a simple-cubic crystal. These values are compared with Monte Carlo results and with values found from the fundamental assumption that thermodynamic quantities such as the specific heat should have singularities at the transition temperature. It turns out that the second-order results are very accurate. Finally then, the method is generalized to give results for fcc, bcc, and hexagonal structures.