Are there incongruent ground states in 2D Edwards-Anderson spin glasses?

Charles Newman, D. L. Stein

Research output: Contribution to journalArticle

Abstract

We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on Z2 are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show -much less likely in our opinion - that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.

Original languageEnglish (US)
Pages (from-to)205-218
Number of pages14
JournalCommunications in Mathematical Physics
Volume224
Issue number1
StatePublished - 2001

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Spin Glass
spin glass
Ground State
ground state
Domain Wall
Zero
Periodic Boundary Conditions
External Field
domain wall
Open Problems
Excitation
Likely
Vary
boundary conditions
Distinct
excitation
temperature
Model

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Are there incongruent ground states in 2D Edwards-Anderson spin glasses? / Newman, Charles; Stein, D. L.

In: Communications in Mathematical Physics, Vol. 224, No. 1, 2001, p. 205-218.

Research output: Contribution to journalArticle

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