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

Abstract

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