Fluctuation Bounds For Interface Free Energies in Spin Glasses

L. P. Arguin; C. M. Newman; D. L. Stein; J. Wehr

doi:10.1007/s10955-014-1009-8

Fluctuation Bounds For Interface Free Energies in Spin Glasses

L. P. Arguin, C. M. Newman, D. L. Stein, J. Wehr

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

12 Scopus citations

Abstract

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.

Original language	English (US)
Pages (from-to)	221-238
Number of pages	18
Journal	Journal of Statistical Physics
Volume	156
Issue number	2
DOIs	https://doi.org/10.1007/s10955-014-1009-8
State	Published - Jul 2014

Keywords

Edwards-Anderson model
Free energy
Spin glasses
Variance bounds

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-014-1009-8

Cite this

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title = "Fluctuation Bounds For Interface Free Energies in Spin Glasses",

abstract = "We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.",

keywords = "Edwards-Anderson model, Free energy, Spin glasses, Variance bounds",

author = "Arguin, {L. P.} and Newman, {C. M.} and Stein, {D. L.} and J. Wehr",

note = "Funding Information: Acknowledgments L.-P. A. is supported by a NSERC discovery grant and a grant FQRNT Nouveaux chercheurs. The research of CMN and DLS is supported in part by US NSF Grants DMS-1207678 and OISE-0730136. J.W. was partially supported by the NSF Grant 0623941.",

year = "2014",

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doi = "10.1007/s10955-014-1009-8",

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T1 - Fluctuation Bounds For Interface Free Energies in Spin Glasses

AU - Arguin, L. P.

AU - Newman, C. M.

AU - Stein, D. L.

AU - Wehr, J.

N1 - Funding Information: Acknowledgments L.-P. A. is supported by a NSERC discovery grant and a grant FQRNT Nouveaux chercheurs. The research of CMN and DLS is supported in part by US NSF Grants DMS-1207678 and OISE-0730136. J.W. was partially supported by the NSF Grant 0623941.

PY - 2014/7

Y1 - 2014/7

N2 - We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.

AB - We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.

KW - Edwards-Anderson model

KW - Free energy

KW - Spin glasses

KW - Variance bounds

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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Fluctuation Bounds For Interface Free Energies in Spin Glasses

Abstract

Keywords

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