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Surfaces and interfaces of lattice models: Mean-field theory as an area-preserving map
Rahul Pandit,Michael Wortis +1 more
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TLDR
Mean field theory for one-dimensional inhomogeneous magnetic systems is formulated as an area-preserving map and its associated boundary conditions are derived for nearest-neighbor Ising interactions as discussed by the authors.Abstract:
Mean-field theory for one-dimensionally inhomogeneous magnetic systems is formulated as an area-preserving map. The map and its associated boundary conditions are derived for nearest-neighbor Ising interactions. The corresponding continuum theory is also constructed. These mappings are two dimensional. Their phase portraits are exhibited and applied to the study of a representative set of surface and interface phenomena, including interfacial structure, surface phase transitions, wetting, prewetting, and layering. The methods developed lend themselves to easy and physical visualization of the types of solutions which the mean-field theory can have, even in rather complex situations. They also make explicit the fundamental differences between continuum mean-field theory (which is integrable) and discrete mean-field theory (which is not).read more
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Surface effects and anchoring in liquid crystals
TL;DR: In this paper, a review focusing on nematic liquid crystals is presented, where three main kinds of effects can be distinguished: the perturbation of the liquid crystalline structure close to the surface, the bulk liquid crystal structure is recovered with an orientation which is fixed by the surface and critical adsorption or wetting can occur at surfaces.
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Walks, walls, wetting, and melting
TL;DR: In this paper, a general mechanism yielding phase transitions in one-dimensional or linear systems is recalled and applied to various wetting and melting phenomena in (d = 2)-dimensional systems, including fluid films and p×1 commensurate adsorbed phases, in which interfaces and domain walls can be modelled by noncrossing walks.
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The ANNNI model — Theoretical analysis and experimental application
TL;DR: The state of the art on the analysis of axial next-nearest neighbor Ising (or ANNNI) models in one, two, and three dimensions is reviewed in this paper.
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Critical point shifts in films
TL;DR: In this article, the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases is discussed.
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Commensurate melting, domain walls, and dislocations
David A. Huse,Michael E. Fisher +1 more