Crossover Scaling and Critical Behavior at the "Surface-Bulk" Multicritical Point

Abstract

With use of a novel Monte Carlo method suited for the study of surface phenomena, the authors have investigated a three-dimensional Ising model with modified surface exchange. The results verify the scaling behavior of the magnetization profile and confirm and extend renormalization-group predictions. The surface-layer magnetization exponent is ${\beta }_1=0.78\mathrm{}\pm 0.02$ except at the "special" (multicritical) transition where ${{\beta }_1}^m=0.175\mathrm{}\pm 0.025$ and the crossover exponent is $\varphi =0.56\mathrm{}\pm 0.04$.