Surface terms on the nishimori line of the Gaussian Edwards-Anderson model

Pierluigi Contucci; Satoshi Morita; Hidetoshi Nishimori

doi:10.1007/s10955-005-8020-z

Surface terms on the nishimori line of the Gaussian Edwards-Anderson model

Pierluigi Contucci, Satoshi Morita, Hidetoshi Nishimori

INF - Applied Information Sciences

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

7 Citations (Scopus)

Abstract

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.

Original language	English
Pages (from-to)	303-312
Number of pages	10
Journal	Journal of Statistical Physics
Volume	122
Issue number	2
DOIs	https://doi.org/10.1007/s10955-005-8020-z
Publication status	Published - 2006 Jan

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Surface terms on the nishimori line of the Gaussian Edwards-Anderson model",

abstract = "For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.",

author = "Pierluigi Contucci and Satoshi Morita and Hidetoshi Nishimori",

note = "Funding Information: One of us (P.C.) thanks Sandro Graffi for introducing him to the surface pressure problems and the Tokyo Institute of Technology for the warm hospitality and the stimulating atmosphere during the visit in which this work was done. This work was supported by the Grant-in-Aid for Scientific Research on Priority Area “Statistical-Mechanical Approach to Probabilistic Information Processing” by the MEXT. P.C. was partially supported by University of Bologna, Funds for Selected Research Topics and Funds for Agreement with Foreign Universities.",

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AU - Contucci, Pierluigi

AU - Morita, Satoshi

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N1 - Funding Information: One of us (P.C.) thanks Sandro Graffi for introducing him to the surface pressure problems and the Tokyo Institute of Technology for the warm hospitality and the stimulating atmosphere during the visit in which this work was done. This work was supported by the Grant-in-Aid for Scientific Research on Priority Area “Statistical-Mechanical Approach to Probabilistic Information Processing” by the MEXT. P.C. was partially supported by University of Bologna, Funds for Selected Research Topics and Funds for Agreement with Foreign Universities.

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N2 - For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.

AB - For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.

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