Phase transitions in finite systems: Influence of geometry on approach towards bulk critical behavior

Abstract

We predict the manner in which a physical system, of size ${\mathrm{L}}^{\mathrm{d}\mathrm{-}\mathrm{d}\mathcal{’}}$×${\mathrm{\infty }}^{\mathrm{d}\mathcal{’}}$, subject to periodic boundary conditions, approaches bulk critical behavior as L→∞. While for T>${\mathrm{T}}_{\mathrm{c}}$(∞) the approach is exponential, for T<${\mathrm{T}}_{\mathrm{c}}$(∞) it is generally governed by power laws whose indices are determined by the bulk exponents for the corresponding d- and d’-dimensional systems. Specific predictions on the spherical model of ferromagnetism and the relativistic Bose gas with pair production are verified by analytical results.