Microscopic approach to orientational order of domain walls

TL;DR

This paper introduces a microscopic statistical mechanics framework to analyze phase transitions and orientational order in two-dimensional stripe-forming Ising systems, revealing nematic and crystal phases.

Contribution

It develops a mean field approach incorporating both density and orientational order parameters, connecting lattice models to continuum Ginzburg-Landau theory.

Findings

Identification of an Ising-nematic phase at low temperatures

Prediction of a crystal-stripe phase at even lower temperatures

Establishment of a link between microscopic models and continuum theories

Abstract

We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified framework. In this work we consider two dimensional stripe forming systems, where nematic, smectic and crystal phases are possible. We introduce a nematic order parameter in a lattice, which measures orientational order of interfaces. We develop a mean field approach which leads to a free energy which is a function of both the magnetization (density) and the orientational (nematic) order parameters. Self-consistent equations for the order parameters are obtained and the solutions are described for a particular system, the Dipolar Frustrated Ising Ferromagnet. We show that this system has an Ising-nematic phase at low temperatures in the square lattice, where positional order (staggered magnetization) is zero. At lower temperatures a crystal-stripe phase may appear. In the continuum limit the present approach connects to a Ginsburg-Landau theory, which has an isotropic-nematic phase transition with breaking of a continuous symmetry.