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

C. M. Newman, D. L. Stein

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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