Hidden scale invariance in the Gay-Berne model

TL;DR

This study demonstrates the existence of hidden scale invariance and isomorphs in the Gay-Berne liquid crystal model, showing invariant dynamics and structure along these curves in the phase diagram, simplifying future theoretical and numerical analyses.

Contribution

The paper provides the first numerical evidence of isomorphs in the Gay-Berne liquid crystal model, revealing hidden scale invariance in both isotropic and nematic phases.

Findings

Strong virial-potential energy correlations indicate hidden scale invariance.

Dynamics and structure are invariant along identified isomorphs.

Invariance is absent along isochores, highlighting the special nature of isomorphs.

Abstract

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity. There we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden-scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the reduced-unit time-autocorrelation functions of the mean-square displacement, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the particles and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.