Interface Structure of the Two-Dimensional, Square Ising Model

Numerical calculations are carried out on the two‐dimensional square Ising model for the structure of the interface between two phases. The method consists of stabilizing the interface in a finite system, calculating interface properties (magnetization profile and surface tension), and then extrapolating to the limit of infinite sized systems where the stabilizing forces may be removed. From the numerical work we make the following tentative conclusions: (1) For temperatures below the critical temperature, the limit of infinite size for fixed magnetic field H $\text{(H 〉0)}$ followed by the limit H→O⁺ does not give rise to an asymptotic degeneracy of eigen values of the transfer matrix. (2) The structure of the interface is sensitive to ``infinitesimal'' forces stabilizing the interface. (3) The surface tension is independent of these same ``infinitesimal'' forces, always being given by the Onsager expression. The first conclusion above implies that an Ising model of infinite size stabilized by an arbitrarily small magnetic field lacks long‐range order.