Competing Interactions, the Renormalization Group and the Isotropic-Nematic Phase Transition

TL;DR

This paper investigates 2D systems with Ising symmetry and competing interactions, revealing how quadrupole interactions influence phase transitions, leading to either first order stripe phases or second order isotropic-nematic transitions.

Contribution

It introduces an analysis of quadrupole interactions within the Renormalization Group framework, highlighting their impact on phase transition types in 2D systems.

Findings

Repulsive quadrupole interactions cause first order stripe phase transitions.

Attractive quadrupole interactions lead to second order isotropic-nematic transitions.

Higher critical temperature observed for attractive quadrupole interactions.

Abstract

We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the Renormalization Group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction term, we analyze the effect of quadrupole interactions in the self consistent Hartree approximation. We show that in the case of repulsive quadrupole interaction, there is a first order phase transition to a stripe phase in agreement with the well known Brazovskii result. However, in the case of attractive quadrupole interactions there is an isotropic-nematic second order transition with higher critical temperature.