Interface formation and a structural phase transition for the spherical model of ferromagnetism

Abstract

A detailed analysis is reported examining the local magnetic susceptibility χ(r), in relation to the correlation functionG(R) and correlation length ζ, of a spherical model ferromagnet confined to geometryΩ =L ^{d −d′} × ∞^d′ (^d′≤2,d>2) under a continuous set oftwisted boundary conditions. The “twist” parameter$\underline \tau$ in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For τ _j →0, ∀j∈d-d′, no seams are present except at infinity, whereas if τ _j = 1/2, impurity saturation occurs. For 0 < τ _j < 1/2 the physical domainΩ _phys =D ^{d −d′} × ∞^d′ (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T ₀). Below that temperature (T>T ₀), seams are frozen at the same position (D≈L/2τ,d-d'=1), revealing a smoothly varying largescale structural phase transition.