Comment on: Competing Interactions, the Renormalization Group, and the Isotropic-Nematic Phase Transition, by D. Barci and D. Stariolo, Phys. Rev. Lett. 98, 200604 (2007)

TL;DR

This paper critiques a recent study on phase transitions in a generalized Brazovskii model, arguing that the claimed striped phase cannot exist in 2D and questioning the conclusions about the isotropic-nematic transition.

Contribution

The author provides a symmetry-based argument showing the non-existence of the striped phase in 2D and challenges the previous analysis of the isotropic-nematic transition's nature.

Findings

Striped phase cannot exist in 2D due to symmetry constraints.

The coarse-grained action used by previous authors is insufficient to determine the transition's nature.

Questions previous claims about the universality class of the isotropic-nematic transition.

Abstract

In a recent PRL Barci and Stariolo (BS) generalized the well known Brazovskii model to include an additional rotationally invariant quartic interaction and study this model in two dimensions (2d). Depending on the parameters of the model, BS find two transitions: a first order isotropic-lamellar (striped) or a second order isotropic-nematic (which they speculate to be in the Kosterlitz-Thouless universality class). Using a simple symmetry argument, I show that the striped phase found by BS can not exist in 2d. Furthermore, I argue that based on the coarse-grained action used by BS it is impossible to reach any conclusion about the nature of the isotropic-nematic transition.