Numerical Study of Finite Size Scaling for First Order Phase Transitions

TL;DR

This paper investigates finite size scaling in 2D Potts models with q=10 and q=20, showing that large lattices are required for asymptotic behavior and that finite size scaling alone cannot confirm first order transitions.

Contribution

It demonstrates that finite size scaling is insufficient to determine the order of phase transitions in certain models, highlighting limitations in current methods.

Findings

Finite size scaling only appears at very large lattice sizes.

Finite size scaling cannot reliably identify first order transitions.

Asymptotic behavior emerges only for extremely large systems.

Abstract

I present results of simulations of the q=10 and q=20 2-d Potts models in the transition region. The asymptotic finite size behavior sets in only for extremely large lattices. We learn from this simulation that finite size scaling cannot be used to decide that a transition is first order.