Finite size scaling and equation of state for Ising lattices

TL;DR

This paper analyzes Monte Carlo data for Ising lattices near the critical point using renormalization group inspired scaling representations, comparing finite size effects and equations of state with experimental data.

Contribution

It introduces two RG-based scaling representations for analyzing Ising lattice data and compares finite size scaling with experimental results.

Findings

Scaling plots show good data collapse across different lattice sizes.

Finite size effects are significant near the critical point.

The equation of state derived matches experimental data for CrBr3.

Abstract

Accurate Monte Carlo data from a set of isotherms near the critical point are analyzed using two RG based complementary representations, given respectively in terms of $\bar h=h/\mid t \mid^{\beta\delta}$ and $\bar \tau=t/h^{1/\beta\delta}$. Scaling plots for data on simple cubic Ising lattices are compared with plots of $ML^{\beta\nu}$ vs. $\mid t \mid L^{1/\nu}$ for increasing $L$ values and with high quality experimental data on $CrBr_{3}$. Finite size effects and the equation of state are discussed.