Interfaces, modulated phases and textures in lattice systems

Abstract

We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be described by a phase-transition energy which we compute by means of variational techniques. Degeneracies due to frustration are also discussed.

References in corpus (4)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
• Checkerboards, stripes and corner energies in spin models with competing interactions
• Domain formation in magnetic polymer composites: an approach via stochastic homogenization
• Realization of stripes and slabs in two and three dimensions

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