Nonperturbative Renormalization Group for the Landau-de Gennes Model

TL;DR

This paper applies the functional renormalization group to the Landau-de Gennes model to analyze the nematic-isotropic phase transition, deriving flow equations and solving them numerically, revealing a first order transition and improving transition temperature estimates.

Contribution

It introduces a nonperturbative renormalization group approach to the Landau-de Gennes model, providing new insights into the nematic-isotropic transition and addressing the NI puzzle.

Findings

Observed a first order phase transition.

Calculated the NI transition temperature difference as 5.85K.

Improved previous estimates of the NI transition temperature.

Abstract

We studied the nematic isotropic phase transition by applying the functional renormalization group to the Landau-de Gennes model. We derived the flow equations for the effective potential as well as the cubic and quartic "couplings" and the anomalous dimension. We then solved the coupled flow equations on a grid using Newton Raphson method. A first order phase transition is observed. We also investigated the nematic isotropic puzzle (the NI puzzle) in this paper. We obtained the NI transition temperature difference ${T_c-T^*}=5.85K$ with sizable improvement over previous results.