Phase Transitions and Static Spin Correlations in Ising Models with Free Surfaces

摘要: Phase transitions in Ising models with tree surfaces are studied from various points of view, including a phenomenological Landau theory, high-temperature series expansions, and scaling theory for thermodynamic quantities correlation functions. In the presence surface number new critical exponents must be defined. These arise because existence "surface" terms functions, anisotropy space lack translational symmetry introduced by surface. The need these already appears which is discussed detail related to microscopic mean-field approximation. essential parameter appearing this an extrapolation length $\ensuremath{\lambda}$ enters boundary condition on magnetization at For magnetic systems order interaction range, contrast superconductors, where it usually much larger. go beyond expansions carried out half-space, tenth two dimensions eighth three dimensions. A developed both functions spin correlations near surface, relations found among half-space. Both numerical calculations compared exact solution half-plane (two dimensions) McCoy Wu, agreement wherever applicable. analogy bulk situation, agree four prediction present work most easily accessible experiment temperature dependence exponent estimated ${\ensuremath{\beta}}_{1}=\frac{2}{3}$. result, ${\ensuremath{\beta}}_{1}=1$, seems more closely presently available experiment, needed clarify situation.