Phase separation at the surface of an Ising ferromagnet

Abraham, D. B.; Issigoni, M.E.

doi:10.1088/0305-4470/13/4/003

Cited by 24 publications

(10 citation statements)

References 10 publications

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“…of (14) with z = α √ 2 for δ = 1/2. For σ a = − σ b = σ + these are precisely the limits obtained from the lattice in [17,9] for the Ising model on the half plane with boundary spins fixed to be positive for |y| > R/2 and negative for |y| < R/2.…”

Section: Interfaces On the Half Planesupporting

confidence: 61%

Interfaces and wetting transition on the half plane. Exact results from field theory

Delfino¹,

Squarcini²

2013

J. Stat. Mech.

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We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties of low energy two-dimensional field theory to determine exact asymptotics of the magnetization profile perperdicularly to the boundary, to show the presence of an interface with endpoints pinned to the boundary, and to determine its passage probability. The midpoint average distance of the interface from the boundary grows as the square root of the distance between the endpoints, unless the reflection amplitude of the bulk excitations on the boundary possesses a stable bound state pole. The contact angle of the phenomenological wetting theory is exactly related to the location of this pole. Results available from the lattice solution of the Ising model are recovered as a particular case.

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Section: Interfaces On the Half Planesupporting

confidence: 61%

Interfaces and wetting transition on the half plane. Exact results from field theory

Delfino¹,

Squarcini²

2013

J. Stat. Mech.

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“…where M = σ + = − σ − > 0 is the spontaneous magnetization. The leading-order term ∝ Υ(χ) shown in (2.22) coincides with scaling limit of exact results obtained for the square lattice Ising model [8,9,41] and from the path-integral formulation of Solid-On-Solid models [11,12]. Within a probabilistic interpretation [19,20] the magnetization profile can be derived by summing over interfacial configurations weighted with a certain passage probability density P 1 (x, y).…”

Section: υ(χ)supporting

confidence: 76%

Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

Squarcini¹,

Tinti²

2021

Preprint

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We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one-and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The analytical results are compared against high-precision Monte Carlo simulations we performed for the specific case of the Ising model. The numerical results are found to be in good agreement with the analytic results in absence of adjustable parameters. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.

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“…termes en e -i.os/T deviennent prépondérants dans (6) et 7 Là encore on retrouve la divergence en 1 t 1obtenue par le calcul exact d'Abraham [7], lorsque T tend vers TR'…”

Section: Système Semi-infini Inhomogène -Consi-unclassified

“…Ce dernier a une plus basse énergie tant que 1 h 1 ;S Ta/s. Il est possible de caractériser sa stabilité de la façon suivante [12] : Supposons qu'au voisinage des points d'ancrage on impose au système d'être dans l'état go(Y); alors, d'après (6) :…”

Section: Function]unclassified

Transition rugueuse et localisation pour une singularité linéaire dans un espace à deux ou trois dimensions

Vallade

Lajzérowicz

1981

J. Phys. France

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2014 Le modèle gaussien continu est utilisé pour décrire les propriétés thermodynamiques de la ligne d'interface dans le modèle d'Ising à deux dimensions ; on retrouve les résultats exacts concernant la transition rugueuse du modèle d'Abraham pour TR ~ Tc On calcule en outre la fonction de corrélation de position des points de l'interface et on étudie l'influence d'un champ extérieur uniforme. Le même modèle est étendu au cas d'une singularité linéaire dans l'espace d = 3 : on montre qu'on peut avoir une transition rugueuse avec une énergie libre possédant une singularité en exp-(A/TR-T).

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Phase separation at the surface of an Ising ferromagnet

Cited by 24 publications

References 10 publications

Interfaces and wetting transition on the half plane. Exact results from field theory

Interfaces and wetting transition on the half plane. Exact results from field theory

Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

Transition rugueuse et localisation pour une singularité linéaire dans un espace à deux ou trois dimensions

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