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

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 $k=k_{\mathrm{opt}}$, ${\epsilon }_{L,k}$ versus $L$ converges to ${\epsilon }_{\infty }$ much faster than $\alpha /L^d$, providing an economic alternative to locate the transition. Moreover, we find that $\alpha \sim \ln k_{\mathrm{opt}}/{\mathcal{L}}_{\infty }$, with ${\mathcal{L}}_{\infty }$ the latent heat density. This suggests that liquid crystals at first-order IN transitions scale approximately as $q$-state Potts models with $q\sim k_{\mathrm{opt}}$.

To appear in Physical Review B