We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ= T C -T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. © EDP Sciences, Società, Italiana di Fisica, Springer-Ver lag 2003.

On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory / Crisanti, Andrea; T., Rizzo; T., Temesvari. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - STAMPA. - 33:2(2003), pp. 203-207. [10.1140/epjb/e2003-00157-8]

On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory

CRISANTI, Andrea;
2003

Abstract

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ= T C -T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. © EDP Sciences, Società, Italiana di Fisica, Springer-Ver lag 2003.
2003
01 Pubblicazione su rivista::01a Articolo in rivista
On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory / Crisanti, Andrea; T., Rizzo; T., Temesvari. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - STAMPA. - 33:2(2003), pp. 203-207. [10.1140/epjb/e2003-00157-8]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/68988
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 16
social impact