Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?

TL;DR

This paper investigates whether critical finite-size scaling functions for the Ising model can be derived solely from universal critical exponents, using a new classification theory and comparing analytical predictions with Monte Carlo simulations.

Contribution

It introduces a new approach to derive universal finite-size scaling functions from critical exponents and validates it with simulation data.

Findings

Good agreement between analytical predictions and Monte Carlo results.

The functional form of the scaling function may be determined by a few universal parameters.

Supports the idea that critical finite-size scaling functions are calculable from critical exponents.

Abstract

Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the critical finite-size scaling functions has been derived by employing a scaling limit that differs from the traditional finite-size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulations. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite-size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.