Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Are There Incongruent Ground States in 2D Edwards–Anderson Spin Glasses? 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

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

Loading next page...
 
/lp/springer-journals/are-there-incongruent-ground-states-in-2d-edwards-anderson-spin-KADJ14eXWg

References (26)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Springer-Verlag Berlin Heidelberg
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Statistical Physics, Dynamical Systems and Complexity; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
DOI
10.1007/PL00005586
Publisher site
See Article on Publisher Site

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.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Jan 25, 2014

There are no references for this article.