A finite-size scaling study of wedge filling transitions in the 3D Ising model

We propose a fully quantitative theory for the finite-size scaling of the filling transition in a three-dimensional double wedge geometry, based on the exact transfer-matrix solution of a phenomenological interfacial model. Antisymmetric fields act at the top and bottom wedges; so each one favours a...

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Bibliographic Details
Published inSoft matter Vol. 9; no. 29; pp. 7069 - 7075
Main Authors Romero-Enrique, José Manuel, Rodríguez-Rivas, Álvaro, Rull, Luis F., Parry, Andrew O.
Format Journal Article
LanguageEnglish
Published 01.01.2013
Subjects
Computer simulation
Ferromagnetism
Ising model
Liquid phases
Magnetization
Mathematical models
Three dimensional
Wedges
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Summary:We propose a fully quantitative theory for the finite-size scaling of the filling transition in a three-dimensional double wedge geometry, based on the exact transfer-matrix solution of a phenomenological interfacial model. Antisymmetric fields act at the top and bottom wedges; so each one favours a different bulk phase under coexistence conditions, i.e.gas and liquid phases in fluid models such as the lattice gas, or equivalently ferromagnetic domains of opposed magnetization in the Ising model. From this formalism we obtain an analytical form for the magnetization probability distribution function at critical filling which is valid for any aspect ratio. To test our predictions we revisit and perform new simulation studies of filling in the Ising model double-wedge geometry and use our finite-size scaling theory to locate accurately the critical filling transition.
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ISSN:1744-683X
1744-6848
DOI:10.1039/c3sm50207d