Winterbottom construction for finite range ferromagnetic models: An double-struck L sign1-approach

T. Bodineau; D. Ioffe; Y. Velenik

doi:10.1023/A:1012277926007

Winterbottom construction for finite range ferromagnetic models: An double-struck L sign₁-approach

T. Bodineau
, D. Ioffe
, Y. Velenik

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair interactions in dimensions greater or equal to 3, and model the substrate by a finite-range boundary magnetic field acting on the spins close to the bottom wall of the box.

Original language	English
Pages (from-to)	93-131
Number of pages	39
Journal	Journal of Statistical Physics
Volume	105
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1012277926007
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

Boundary Gibbs fields
Equilibrium crystal shapes
Ferromagnetic lattice models
Winterbottom construction
Wulff construction

Access to Document

10.1023/A:1012277926007

Cite this

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title = "Winterbottom construction for finite range ferromagnetic models: An double-struck L sign1-approach",

abstract = "We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair interactions in dimensions greater or equal to 3, and model the substrate by a finite-range boundary magnetic field acting on the spins close to the bottom wall of the box.",

keywords = "Boundary Gibbs fields, Equilibrium crystal shapes, Ferromagnetic lattice models, Winterbottom construction, Wulff construction",

author = "T. Bodineau and D. Ioffe and Y. Velenik",

year = "2001",

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AU - Bodineau, T.

AU - Ioffe, D.

AU - Velenik, Y.

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N2 - We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair interactions in dimensions greater or equal to 3, and model the substrate by a finite-range boundary magnetic field acting on the spins close to the bottom wall of the box.

AB - We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair interactions in dimensions greater or equal to 3, and model the substrate by a finite-range boundary magnetic field acting on the spins close to the bottom wall of the box.

KW - Boundary Gibbs fields

KW - Equilibrium crystal shapes

KW - Ferromagnetic lattice models

KW - Winterbottom construction

KW - Wulff construction

U2 - 10.1023/A:1012277926007

DO - 10.1023/A:1012277926007

M3 - Article

AN - SCOPUS:0035486314

SN - 0022-4715

VL - 105

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EP - 131

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2