Thermal melting of density waves on the square lattice

TL;DR

This paper develops a theoretical framework for understanding how thermal fluctuations influence the melting of commensurate density waves on a square lattice, revealing transitions to incommensurate states and critical points.

Contribution

It introduces a comprehensive theory for thermal melting of p x p density waves, including the nature of phase transitions and critical behavior for specific cases like p=4.

Findings

Adjacent incommensurate striped states emerge during melting.

The 4x4 commensurate state can melt directly into a disordered phase.

Identification of a self-dual critical point with non-universal exponents.

Abstract

We present the theory of the effect of thermal fluctuations on commensurate "p x p" density wave ordering on the square lattice (p >= 3, integer). For the case in which this order is lost by a second order transition, we argue that the adjacent state is generically an incommensurate striped state, with commensurate p-periodic long range order along one direction, and incommensurate quasi-long-range order along the orthogonal direction. We also present the routes by which the fully disordered high temperature state can be reached. For p=4, and at special commensurate densities, the "4 x 4" commensurate state can melt directly into the disordered state via a self-dual critical point with non-universal exponents.