Microscopic approach to orientational order of domain walls

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.

9 pages, 7 figures, revised and expanded, published version

References in corpus (7)

• Soft Spheres Make More Mesophases
• Phase diagram of an Ising model for ultrathin magnetic films
• (Ir-)Reversibility and thermal equilibrium in magnetic domain pattern formation in ultra-thin ferromagnetic films
• Orientational order in two dimensions from competing interactions at different scales
• Stripe width and non-local domain walls in the two-dimensional Dipolar Frustrated Ising Ferromagnet
• Competing Interactions, the Renormalization Group and the Isotropic-Nematic Phase Transition
• Inverse transition in the two dimensional dipolar frustrated ferromagnet

Cited by in corpus (9)

• Long-range interacting quantum systems
• Nematic phase in the J${}_1$-J${}_2$ square lattice Ising model in an external field
• The nematic phase in stripe forming systems within the self consistent screening approximation
• Pair correlations and structure factor of the $J_1$-$J_2$ square lattice Ising model in an external field within the Cluster Variation Method
• Nematic Phase in two-dimensional frustrated systems with power law decaying interactions
• Detecting composite orders in layered models via machine learning
• Stochastic dynamics of planar magnetic moments in a three-dimensional environment
• Dynamics of a Liquid Crystal close to the Fréedericksz transition
• Glassy behavior of two-dimensional stripe-forming systems