AN INVESTIGATION OF FINITE-SIZE SCALING FOR SYSTEMS WITH LONG-RANGE INTERACTION - THE SPHERICAL MODEL

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distances r as r-d -σ, where d is the space dimensionality and σ>0. It allows for a unified treatment of short-range (σ=2) and long-range (σ<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometry Ld-d′×∞d′ subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values of d≥σ, 0≤d′≤σ. It is shown that the ε-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities. © 1990 Plenum Publishing Corporation.