Numerical Computation of Finite Size Scaling Functions: An Alternative Approach to Finite Size Scaling

TL;DR

This paper introduces a new method for computing finite size scaling functions using Monte Carlo simulations, enabling accurate estimation of critical parameters and exponents across different system sizes.

Contribution

It presents an alternative approach to finite size scaling that relies solely on the variable x = ξ_L / L, improving accuracy in critical parameter estimation.

Findings

Finite size scaling functions show excellent data collapse.

Critical temperatures and exponents are estimated with high accuracy.

Renormalized four-point coupling constants support hyperscaling.

Abstract

Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = \xi_L / L$, where $\xi_L$ is the correlation length in a finite system of size $L$. Data for the d=2 and d=3 Ising models, taken at different temperatures and for different size lattices, show excellent data collapse over the entire range of scaling variable for susceptibility and correlation length. From these finite size scaling functions we can estimate critical temperatures and exponents with rather high accuracy even though data are not obtained extremely close to the critical point. The bulk values of the renormalized four-point coupling constant are accurately measured and show strong evidence for hyperscaling.