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

Douglas Abraham, Charles Newman, Senya Shlosman

Research output: Contribution to journalArticle

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 (Formula presented.); here (Formula presented.) 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 (Formula presented.) by developing new Ising exact solution results—in particular, there is at least one pure state for each (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalJournal of Statistical Physics
DOIs
StateAccepted/In press - Nov 13 2017

Fingerprint

Pure State
Half-plane
Ising model
Ising Model
Continuum
continuums
Ising
Angle
Gibbs States
half planes
Ferromagnet
Exact Solution
Configuration
configurations

Keywords

  • Exact solutions
  • Extremal state
  • Ising model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A Continuum of Pure States in the Ising Model on a Halfplane. / Abraham, Douglas; Newman, Charles; Shlosman, Senya.

In: Journal of Statistical Physics, 13.11.2017, p. 1-16.

Research output: Contribution to journalArticle

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