arXiv 0906.41662009-06-23cond-mat.stat-mech

一级各向同性到一级各向异性转变的晶体尺寸效应

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

J. M. Fish, R. L. C. Vink

备注：: To appear in Physical Review B

摘要：

本文给出了液晶晶格模型中一阶各向同性到相变的模拟数据，并通过有限尺寸标度确定了相变温度的热力学极限$ε_\infty$。我们观察到，比热最大值的逆温度可以一致地外推到$ε_\infty$，假设通常的$α/ L^d$依赖性，与$L$的系统大小，$d$的晶格尺寸和比例常数$α$。我们还调查了数量$ε_{L,k}$，有限尺寸的逆温度，其中$k$是各向同性相的重量比。对于最佳值$k = k_{\rm opt}$，$ε_{L,k}$与$L$收敛到$ε_\infty$的速度比$α/L^d$快得多，从而提供了定位过渡的经济替代方案。此外，我们发现，$α\sim \ln k_{\rm opt} / {\cal L}_\infty$，与${\cal L}_\infty$的潜热密度。这表明，液晶在一阶IN转变的比例近似为$q$状态Potts模型与$q \sim k_{\rm opt}$。

英文摘要：

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 $ε_\infty$ via finite-size scaling. We observe that the inverse temperature of the specific heat maximum can be consistently extrapolated to $ε_\infty$ assuming the usual $α/ L^d$ dependence, with $L$ the system size, $d$ the lattice dimension and proportionality constant $α$. 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 $k = k_{\rm opt}$, $ε_{L,k}$ versus $L$ converges to $ε_\infty$ much faster than $α/L^d$, providing an economic alternative to locate the transition. Moreover, we find that $α\sim \ln k_{\rm opt} / {\cal L}_\infty$, 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 $q \sim k_{\rm opt}$.

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英文摘要：

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