# Finite-size effects at first-order isotropic-to-nematic transitions - Condensed Matter > Statistical Mechanics

Finite-size effects at first-order isotropic-to-nematic transitions - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We present simulation data of first-order isotropic-to-nematic transitions inlattice models of liquid crystals and locate the thermodynamic limit inversetransition temperature $\epsilon \infty$ via finite-size scaling. We observethat the inverse temperature of the specific heat maximum can be consistentlyextrapolated to $\epsilon \infty$ assuming the usual $\alpha - L^d$ dependence,with $L$ the system size, $d$ the lattice dimension and proportionalityconstant $\alpha$. We also investigate the quantity $\epsilon {L,k}$, thefinite-size inverse temperature where $k$ is the ratio of weights of theisotropic to nematic phase. For an optimal value $k = k { m opt}$,$\epsilon {L,k}$ versus $L$ converges to $\epsilon \infty$ much faster than$\alpha-L^d$, providing an economic alternative to locate the transition.Moreover, we find that $\alpha \sim \ln k { m opt} - {\cal L} \infty$, with${\cal L} \infty$ the latent heat density. This suggests that liquid crystalsat first-order IN transitions scale approximately as $q$-state Potts modelswith $q \sim k { m opt}$.

Author: ** J.M. Fish, R.L.C. Vink**

Source: https://arxiv.org/