A Continuum of Pure States in the Ising Model on a Halfplane View Full Text


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Article Info

DATE

2018-07

AUTHORS

Douglas Abraham, Charles M. Newman, Senya Shlosman

ABSTRACT

We study the homogeneous nearest–neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition—say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature T, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle θ∈[-π/2,+π/2]; here θ specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to T=Tc by developing new Ising exact solution results—in particular, there is at least one pure state for each θ. More... »

PAGES

611-626

References to SciGraph publications

  • 1976-02. Interface profile of the Ising ferromagnet in two dimensions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1990-03. Extremity of the disordered phase in the Ising model on the Bethe lattice in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2012-09. A Manifold of Pure Gibbs States of the Ising Model on a Cayley Tree in JOURNAL OF STATISTICAL PHYSICS
  • 1986-03. Uniqueness and half-space nonuniqueness of gibbs states in Czech models in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1999-01. “Non-Gibbsian” States and their Gibbs Description in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-11. Ising model in half-space: A series of phase transitions in low magnetic fields in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1980-05. Translation invariance and instability of phase coexistence in the two dimensional Ising system in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1998-03. Nonperiodic Long-Range Order for Fast-Decaying Interactions at Positive Temperatures in JOURNAL OF STATISTICAL PHYSICS
  • 1969-09. Observables at infinity and states with short range correlations in statistical mechanics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-03. Interaction Versus Entropic Repulsion for Low Temperature Ising Polymers in JOURNAL OF STATISTICAL PHYSICS
  • 1990-12. Breaking of periodicity at positive temperatures in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-03. Ornstein-Zernike theory for finite range Ising models above Tc in PROBABILITY THEORY AND RELATED FIELDS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-017-1918-4

    DOI

    http://dx.doi.org/10.1007/s10955-017-1918-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092666551


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