Phase Diagram of a Generalized ABC Model on the Interval

J. Barton; J. L. Lebowitz; E. R. Speer

doi:10.1007/s10955-011-0279-7

Phase Diagram of a Generalized ABC Model on the Interval

J. Barton, J. L. Lebowitz, E. R. Speer

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4 Scopus citations

Abstract

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,...,N is occupied by a particle of type α=A,B,C, with the average density of each particle species N_α/N=r_α fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρ_α(x) except for some special values of the r_α for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.

Original language	English (US)
Pages (from-to)	763-784
Number of pages	22
Journal	Journal of Statistical Physics
Volume	145
Issue number	3
DOIs	https://doi.org/10.1007/s10955-011-0279-7
State	Published - Nov 2011

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

External fields
Generalized ABC model
Phase diagram
Scaling limit

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10.1007/s10955-011-0279-7

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title = "Phase Diagram of a Generalized ABC Model on the Interval",

abstract = "We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,...,N is occupied by a particle of type α=A,B,C, with the average density of each particle species Nα/N=rα fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρα(x) except for some special values of the rα for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.",

keywords = "External fields, Generalized ABC model, Phase diagram, Scaling limit",

author = "J. Barton and Lebowitz, {J. L.} and Speer, {E. R.}",

note = "Funding Information: Acknowledgements We thank Lorenzo Bertini, Thierry Bodineau, Bernard Derrida, David Mukamel, and Oliver Penrose for useful discussions. The work of J.B. and J.L.L. was supported in part by NSF grant DMR-08-02120 and AFOSR grant FA-95550-10-1-0131.",

year = "2011",

month = nov,

doi = "10.1007/s10955-011-0279-7",

language = "English (US)",

volume = "145",

pages = "763--784",

journal = "Journal of Statistical Physics",

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AU - Barton, J.

AU - Lebowitz, J. L.

AU - Speer, E. R.

N1 - Funding Information: Acknowledgements We thank Lorenzo Bertini, Thierry Bodineau, Bernard Derrida, David Mukamel, and Oliver Penrose for useful discussions. The work of J.B. and J.L.L. was supported in part by NSF grant DMR-08-02120 and AFOSR grant FA-95550-10-1-0131.

PY - 2011/11

Y1 - 2011/11

N2 - We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,...,N is occupied by a particle of type α=A,B,C, with the average density of each particle species Nα/N=rα fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρα(x) except for some special values of the rα for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.

AB - We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,...,N is occupied by a particle of type α=A,B,C, with the average density of each particle species Nα/N=rα fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρα(x) except for some special values of the rα for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.

KW - External fields

KW - Generalized ABC model

KW - Phase diagram

KW - Scaling limit

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3

ER -

Phase Diagram of a Generalized ABC Model on the Interval

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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