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

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 $p<p_t$, the transition is of the Kosterlitz-Thouless type, while 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.