On the finite-size behavior of systems with asymptotically large critical shift

TL;DR

This paper derives exact finite-size scaling functions for the susceptibility in three-dimensional mean spherical model films with various boundary conditions, revealing how finite-size effects influence critical behavior near the phase transition.

Contribution

It provides explicit analytical results for the finite-size susceptibility and scaling functions, including their asymptotics, for different boundary conditions in the mean spherical model.

Findings

Explicit finite-size scaling functions derived for different boundary conditions.

Asymptotic behavior of scaling functions near and above the critical temperature.

Finite-size critical temperature shift exponent is smaller than 1/nu.

Abstract

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.