Finite-size effects at first-order isotropic-to-nematic transitions

TL;DR

This paper uses finite-size scaling in simulations of liquid crystal models to accurately determine the transition temperature and explores how the transition properties relate to Potts models, revealing new scaling behaviors.

Contribution

It introduces a novel finite-size scaling method to locate the transition temperature and links liquid crystal transitions to Potts model scaling.

Findings

Inverse transition temperature can be extrapolated using specific heat maxima.

Optimal phase weight ratio accelerates convergence to the thermodynamic limit.

Transition scaling relates to Potts model q-value via latent heat density.

Abstract

We present simulation data of first-order isotropic-to-nematic transitions in lattice models of liquid crystals and locate the thermodynamic limit inverse transition temperature $\epsilon_\infty$ via finite-size scaling. We observe that the inverse temperature of the specific heat maximum can be consistently extrapolated to $\epsilon_\infty$ assuming the usual $\alpha / L^d$ dependence, with $L$ the system size, $d$ the lattice dimension and proportionality constant $\alpha$. We also investigate the quantity $\epsilon_{L,k}$, the finite-size inverse temperature where $k$ is the ratio of weights of the isotropic to nematic phase. For an optimal value $k = k_{\rm opt}$, $\epsilon_{L,k}$ versus $L$ converges to $\epsilon_\infty$ much faster than $\alpha/L^d$, providing an economic alternative to locate the transition. Moreover, we find that $\alpha \sim \ln k_{\rm opt} / {\cal L}_\infty$, with ${\cal L}_\infty$ the latent heat density. This suggests that liquid crystals at first-order IN transitions scale approximately as $q$-state Potts models with $q \sim k_{\rm opt}$.