Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?

Details Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses? Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?

2001-03-19

arxiv.org/abs/cond-mat/0103395v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages (LaTeX); 1 figure; minor revisions; to appear in Commun. Math. Phys

Scientific paper

10.1007/PL00005586

We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) 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 the infinite square lattice 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.

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