Local order at arbitrary distances in finite-dimensional spin-glass models

Pierluigi Contucci; Francesco Unguendoli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2005)

  • Volume: 16, Issue: 3, page 197-202
  • ISSN: 1120-6330

Abstract

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For a finite dimensional spin-glass model we prove low temperature local order i.e. the property of concentration of the overlap distribution close to the value 1. The theorem hold for both local observables and for products of observables at arbitrary mutual distance: when the Hamiltonian includes the Edwards-Anderson interaction we prove bond local order, when it includes the random-field interaction we prove site local order.

How to cite

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Contucci, Pierluigi, and Unguendoli, Francesco. "Local order at arbitrary distances in finite-dimensional spin-glass models." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.3 (2005): 197-202. <http://eudml.org/doc/252376>.

@article{Contucci2005,
abstract = {For a finite dimensional spin-glass model we prove low temperature local order i.e. the property of concentration of the overlap distribution close to the value 1. The theorem hold for both local observables and for products of observables at arbitrary mutual distance: when the Hamiltonian includes the Edwards-Anderson interaction we prove bond local order, when it includes the random-field interaction we prove site local order.},
author = {Contucci, Pierluigi, Unguendoli, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Spin-glasses; Local order; Overlap distribution},
language = {eng},
month = {9},
number = {3},
pages = {197-202},
publisher = {Accademia Nazionale dei Lincei},
title = {Local order at arbitrary distances in finite-dimensional spin-glass models},
url = {http://eudml.org/doc/252376},
volume = {16},
year = {2005},
}

TY - JOUR
AU - Contucci, Pierluigi
AU - Unguendoli, Francesco
TI - Local order at arbitrary distances in finite-dimensional spin-glass models
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/9//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 3
SP - 197
EP - 202
AB - For a finite dimensional spin-glass model we prove low temperature local order i.e. the property of concentration of the overlap distribution close to the value 1. The theorem hold for both local observables and for products of observables at arbitrary mutual distance: when the Hamiltonian includes the Edwards-Anderson interaction we prove bond local order, when it includes the random-field interaction we prove site local order.
LA - eng
KW - Spin-glasses; Local order; Overlap distribution
UR - http://eudml.org/doc/252376
ER -

References

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  1. MEZARD, M. - PARISI, G. - VIRASORO, M.A., Spin glass theory and beyond. World Scien., 1987. Zbl0992.82500MR1026102
  2. FISHER, D.S. - HUSE, D.H., Ordered Phase of Short-Range Ising Spin-Glasses. Phys. Rev. Lett., 56, 1986, 1601-1604. 
  3. NEWMNAN, C.M. - STEIN, D.L., Ordering and broken symmetry in short-ranged spin glasses. J. Phys.: Condens. Matter, 15, 2003, R1319-R1364; http://arxiv.org/abs/cond-mat/0301403. 
  4. EDWARDS, S.F. - ANDERSON, P.W., Theory of spin glasses. J. Phys. F., 5, May 1975, 965-974. 
  5. ZEGARLINSKI, B., Interactions and pressure functionals for disordered lattice systems. Comm. Math. Phys., 139, 1991, 305-339. Zbl0747.58066MR1120141
  6. RUELLE, D., Statistical Mechanics, Rigorous Results. W.A. Benjamin, New York1969. Zbl0177.57301MR289084
  7. CONTUCCI, P. - GRAFFI, S., Monotonicity and Thermodynamic Limit for Short Range Disordered Models. J. Stat. Phys., 115, Nos. 1/2, 2004, 581-589. Zbl1157.82337MR2070108DOI10.1023/B:JOSS.0000019812.03696.b7
  8. SCHULTZ, T.D. - MATTIS, D.C. - LIEB, E.H., Two-Dimensional Ising Model as a Soluble Problem of Many Fermions. Rev. Mod. Phys., 36, 1964, 856-871. MR180274
  9. GUERRA, F., About the Overlap Distribution in Mean Field Spin Glass Mod. Int. Jou. Mod. Phys. B, 10, 1997, 1675-1684. Zbl1229.82097MR1405193DOI10.1142/S0217979296000751
  10. NEWMNAN, C.M. - STEIN, D.L., Multiple states and thermodynamic limits in short-ranged Ising spin-glass models. Phys. Rev. B, 46, 1992, 973-982. 

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