Communications in Mathematical Physics

, Volume 300, Issue 3, pp 641–657 | Cite as

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

  • Louis-Pierre Arguin
  • Michael DamronEmail author
  • C. M. Newman
  • D. L. Stein


We consider the Edwards-Anderson Ising spin glass model on the half-plane \({\mathbb{Z} \times \mathbb{Z}^+}\) 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 \({\mathcal{K}(J,\alpha)}\) 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 \({\mathcal{K}(\alpha\,|\,J)}\) is supported on a single ground state pair.


Excited State Domain Wall Spin Glass Conditional Measure Spin Glass Model 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Louis-Pierre Arguin
    • 1
  • Michael Damron
    • 2
    Email author
  • C. M. Newman
    • 1
  • D. L. Stein
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  3. 3.Courant Institute of Mathematical Sciences and Physics DepartmentNew York UniversityNew YorkUSA

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