Exotic states in long-range spin glasses
Abstract
We consider Ising spin glasses onZd with couplingsJxy=cy-xZxy, where thecy's are nonrandom real coefficients and theZxy's are independent, identically distributed random variables withE[Zxy]=0 andE[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|2=∞, then (with probability one) there are uncountably many (infinite volume) ground states $$\tilde \sigma $$ , each of which has the following property: forany temperatureT<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from $$\tilde \sigma $$ only atfinitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- October 1993
- DOI:
- 10.1007/BF02099766
- Bibcode:
- 1993CMaPh.157..371G
- Keywords:
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- Boundary Condition;
- Neural Network;
- Statistical Physic;
- Complex System;
- Nonlinear Dynamics