2014/01/31 by R. L. C. Vink, Richard L. C. Vink
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Extrapolation #Geometry #Isotropy #Kosterlitz–Thouless transition #Liquid Crystal Research Advancements #Liquid crystal #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Monte Carlo method #Order (exchange) #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #Transition point #Tricritical point #Type (biology) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.062132
published as Phys. Rev. E V90 P062132 (2014) · 8 pages, 8 figures
openalex publication_date 2014/12/22 · arxiv created 2014/12/28 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Liquid crystals in two dimensions do not support long-range nematic order, but a quasinematic phase where the orientational correlations decay algebraically is possible. The transition from the isotropic to the quasinematic phase can be continuous and 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 quasinematic 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.