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arXiv · 1401.6301

Crossover from a Kosterlitz-Thouless to a discontinuous phase transition in two-dimensional liquid crystals

Richard L. C. Vink
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Abstract

Liquid crystals in two dimensions do not support long-ranged nematic order, but a quasi-nematic phase where the orientational correlations decay algebraically is possible. The transition from the isotropic to the quasi-nematic phase can be continuous of the Kosterlitz-Thouless type, or it can be first-order. We report here on a liquid crystal model where the nature of the isotropic to quasi-nematic transition can be tuned via a single parameter $p$ in the pair potential. For $p p_t$ it is first-order. Precisely at $p=p_t$, there is a tricritical point, where, in addition to the orientational correlations, also the positional correlations decay algebraically. The tricritical behavior is analyzed in detail, including an accurate estimate of $p_t$. The results follow from extensive Monte Carlo simulations combined with a finite-size scaling analysis. Paramount in the analysis is a scheme to facilitate the extrapolation of simulation data in parameters that are not necessarily field variables (in this case the parameter $p$) the details of which are also provided. This scheme provides a simple and powerful alternative for situations where standard histogram reweighting cannot be applied.

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BibTeXRIS

Richard L. C. Vink. 2014-01-24. Crossover from a Kosterlitz-Thouless to a discontinuous phase transition in two-dimensional liquid crystals. https://doi.org/10.1103/physreve.90.062132

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