Exotic states in long-range spin glasses

A. Gandolfi; C. M. Newman; D. L. Stein

doi:10.1007/BF02099766

Exotic states in long-range spin glasses

A. Gandolfi, C. M. Newman, D. L. Stein

Research output: Contribution to journal › Article › peer-review

Abstract

We consider Ising spin glasses on Z^d with couplings J_xy=c_y-xZ_xy, where the c_y's are nonrandom real coefficients and the Z_xy's are independent, identically distributed random variables with E[Z_xy]=0 and E[Z_xy²]=1. We prove that if ∑_y|c_y|=∞ while ∑_y|c_y|²=∞, then (with probability one) there are uncountably many (infinite volume) ground states {Mathematical expression}, each of which has the following property: for any temperature T<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from {Mathematical expression} only at finitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.

Original language	English (US)
Pages (from-to)	371-387
Number of pages	17
Journal	Communications In Mathematical Physics
Volume	157
Issue number	2
DOIs	https://doi.org/10.1007/BF02099766
State	Published - Oct 1993

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We consider Ising spin glasses on Zd with couplings Jxy=cy-xZxy, where the cy's are nonrandom real coefficients and the Zxy's are independent, identically distributed random variables with E[Zxy]=0 and E[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|2=∞, then (with probability one) there are uncountably many (infinite volume) ground states {Mathematical expression}, each of which has the following property: for any temperature T<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from {Mathematical expression} only at finitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.",

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AU - Stein, D. L.

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N2 - We consider Ising spin glasses on Zd with couplings Jxy=cy-xZxy, where the cy's are nonrandom real coefficients and the Zxy's are independent, identically distributed random variables with E[Zxy]=0 and E[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|2=∞, then (with probability one) there are uncountably many (infinite volume) ground states {Mathematical expression}, each of which has the following property: for any temperature T<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from {Mathematical expression} only at finitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.

AB - We consider Ising spin glasses on Zd with couplings Jxy=cy-xZxy, where the cy's are nonrandom real coefficients and the Zxy's are independent, identically distributed random variables with E[Zxy]=0 and E[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|2=∞, then (with probability one) there are uncountably many (infinite volume) ground states {Mathematical expression}, each of which has the following property: for any temperature T<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from {Mathematical expression} only at finitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.

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Exotic states in long-range spin glasses

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