Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model

E.M.N. Cirillo; Vanessa Jacquier; Cristian Spitoni

doi:10.1016/j.physd.2024.134125

Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model

E.M.N. Cirillo, Vanessa Jacquier, Cristian Spitoni

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Abstract

We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically the metastability scenarios. In particular we show that, depending on the parameters of the model, the stable phase nucleation can be either homogeneous or heterogeneous. Notably, heterogeneous nucleation is proved in the region of the parameter space where the chemical potential is larger than the external magnetic field.

Original language	English
Article number	134125
Journal	Physica D: Nonlinear Phenomena
Volume	461
DOIs	https://doi.org/10.1016/j.physd.2024.134125
Publication status	Published - May 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

Funding

ENMC acknowledges that this work has been done under the framework of GNMF and PRIN 2022 project “Mathematical modelling of heterogeneous systems”. VJ thanks GNAMPA (CUP B53D23009360006). ENMC acknowledges that this work has been done under the framework of GNMF and PRIN 2022 project “Mathematical modelling of heterogeneous systems”. VJ thanks GNAMPA (CUP B53D23009360006 ).

Funders	Funder number
GNMF
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni	CUP B53D23009360006

Keywords

Blume–Capel model
Effect of boundary conditions
Glauber dynamics
Low temperature dynamics
Metastability
Nucleation

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1-s2.0-S0167278924000769-mainFinal published version, 1.42 MBLicence: CC BY

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title = "Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model",

abstract = "We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically the metastability scenarios. In particular we show that, depending on the parameters of the model, the stable phase nucleation can be either homogeneous or heterogeneous. Notably, heterogeneous nucleation is proved in the region of the parameter space where the chemical potential is larger than the external magnetic field.",

keywords = "Blume–Capel model, Effect of boundary conditions, Glauber dynamics, Low temperature dynamics, Metastability, Nucleation",

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T1 - Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model

AU - Cirillo, E.M.N.

AU - Jacquier, Vanessa

AU - Spitoni, Cristian

PY - 2024/5

Y1 - 2024/5

N2 - We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically the metastability scenarios. In particular we show that, depending on the parameters of the model, the stable phase nucleation can be either homogeneous or heterogeneous. Notably, heterogeneous nucleation is proved in the region of the parameter space where the chemical potential is larger than the external magnetic field.

AB - We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically the metastability scenarios. In particular we show that, depending on the parameters of the model, the stable phase nucleation can be either homogeneous or heterogeneous. Notably, heterogeneous nucleation is proved in the region of the parameter space where the chemical potential is larger than the external magnetic field.

KW - Blume–Capel model

KW - Effect of boundary conditions

KW - Glauber dynamics

KW - Low temperature dynamics

KW - Metastability

KW - Nucleation

UR - https://www.scopus.com/pages/publications/85186959191

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DO - 10.1016/j.physd.2024.134125

M3 - Article

SN - 0167-2789

VL - 461

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

M1 - 134125

ER -

Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model

Abstract

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Keywords

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