Symmetry breaking in frustrated systems: effective fluctuation spectrum due to coupling effects

TL;DR

This paper investigates how symmetry breaking in frustrated systems leads to an anisotropic fluctuation spectrum due to mode coupling, affecting phase transition nature and order parameters.

Contribution

It introduces an analysis of coupling effects on fluctuation spectra in frustrated systems, revealing continuous modulated solutions in three dimensions.

Findings

Continuous modulated solutions in d=3

Discontinuous transitions for d<3

Analytical expressions for order parameters

Abstract

We study the Langevin dynamics of a d-dimensional Ginzburg-Landau Hamiltonian with isotropic long range repulsive interactions. We show that, once the symmetry is broken, there is a coupling between the mean value of the local field and its fluctuations, generating an anisotropic effective fluctuation spectrum. This anisotropy has many interesting dynamical consequences. In the infinite time limit, static results are recovered which can be compared with the well known Brazovskii's transition to a state with modulated order. Our study reveals that the modulated solution appears continuously in d = 3 contrary to what is found in the usual approach neglecting coupling of modes, while for d < 3 transitions are still discontinuous. Analytical results for positional and orientational order parameters are also obtained and interpreted in the context of recent discussions.