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Non-translation invariant Gibbs states with coexisting phases

I. Existence of sharp interface for Widom-Rowlinson type lattice models in three dimensions

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Abstract

We investigate the spatially inhomogeneous states of two component,A - B, Widom-Rowlinson type lattice systems. When the fugacity of the two components are equal and large, these systems can exist in two different homogeneous (translation invariant) pure phases oneA-rich and oneB-rich. We consider now the system in a box with boundaries favoring the segregation of these two phases into “top and bottom” parts of the box. Utilizing methods due to Dobrushin we prove the existence, in three or more dimensions, of a “sharp” interface for the system which persists in the limit of the size of the box going to infinity. We also give some background on rigorous results for the interface problem in Ising spin systems.

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Author notes

  1. Enzo Olivieri

    Present address: Istituto Matematico, Universita di Roma, GNFM, I-Roma, Italy

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    Jean Bricmont, Joel L. Lebowitz, Charles E. Pfister & Enzo Olivieri

Authors
  1. Jean Bricmont
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  2. Joel L. Lebowitz
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  3. Charles E. Pfister
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  4. Enzo Olivieri
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Additional information

Communicated by J. Glimm

Supported in part by NSF Grant PHY 77-22302

Supported by the Swiss National Foundation for Scientific Research

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Bricmont, J., Lebowitz, J.L., Pfister, C.E. et al. Non-translation invariant Gibbs states with coexisting phases. Commun.Math. Phys. 66, 1–20 (1979). https://doi.org/10.1007/BF01197743

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  • DOI: https://doi.org/10.1007/BF01197743

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