Scaling Function for the Critical Specific Heat in a Confined Geometry : Spherical Limit

TL;DR

This paper derives an exact scaling function for the critical specific heat in a spherical limit, effectively describing experimental data near the superfluid transition in confined geometries.

Contribution

It provides an exact analytical form of the scaling function for the critical specific heat above the transition temperature, generalized to arbitrary specific heat exponents.

Findings

Excellent agreement with experimental data of Mehta and Gasparini

Validates the spherical limit as a useful model for confined critical phenomena

Offers a precise analytical tool for studying superfluid transitions

Abstract

The scaling function for the critical specific heat is obtained exactly for temperatures above the bulk transition temperature by working in the spherical limit. Generalization of the function to arbitrary $\alpha$ (the specific heat exponent), gives an excellent account of the experimental data of Mehta and Gasparini near the superfluid transition.