Universal Finite-Size-Scaling Functions

TL;DR

This paper demonstrates that finite-size-scaling functions of the Ising model are universal across different lattice types, including quasiperiodic lattices, by collapsing data onto a single curve using nonuniversal scaling factors.

Contribution

It extends the concept of universal finite-size-scaling functions to various lattice types and the order-parameter distribution, considering boundary condition effects.

Findings

Finite-size-scaling functions collapse onto a single curve across lattices.

Universality extends to quasiperiodic lattices like Penrose.

Boundary conditions influence the scaling functions.

Abstract

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions. Keywords: Universal Finite-Size-Scaling Function; Ising Model; Order-Parameter Probability Distribution Function.