Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

Louis Pierre Arguin, Michael Damron, C. M. Newman, D. L. Stein

Research output: Contribution to journalArticle

Abstract

We consider the Edwards-Anderson Ising spin glass model on the half-plane ℤ × ℤ+ with zero external field and a wide range of choices, including mean zero Gaussian for the common distribution of the collection J of i. i. d. nearest neighbor couplings. The infinite-volume joint distribution K(J,α) of couplings J and ground state pairs α with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution K(α{pipe} J) is supported on a single ground state pair.

Original languageEnglish (US)
Pages (from-to)641-657
Number of pages17
JournalCommunications In Mathematical Physics
Volume300
Issue number3
DOIs
StatePublished - Dec 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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