We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h > 0 and Tc(h) < T < Tc(h = 0), of the d = 1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field.

Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field) / Dilucca, M.; Leuzzi, L.; Parisi, G.; Ricci-Tersenghi, F.; Ruiz-Lorenzo, J. J.. - In: ENTROPY. - ISSN 1099-4300. - 22:2(2020), p. 250. [10.3390/e22020250]

Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)

Dilucca M.;Leuzzi L.;Parisi G.;Ricci-Tersenghi F.;Ruiz-Lorenzo J. J.
2020

Abstract

We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h > 0 and Tc(h) < T < Tc(h = 0), of the d = 1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field.
2020
Disordered systems; Mean field; Numerical simulations; Phase transitions; Spin glasses
01 Pubblicazione su rivista::01a Articolo in rivista
Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field) / Dilucca, M.; Leuzzi, L.; Parisi, G.; Ricci-Tersenghi, F.; Ruiz-Lorenzo, J. J.. - In: ENTROPY. - ISSN 1099-4300. - 22:2(2020), p. 250. [10.3390/e22020250]
File allegati a questo prodotto
File Dimensione Formato  
Dilucca_Spin Glasses in a Field Show_2020.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.67 MB
Formato Adobe PDF
1.67 MB Adobe PDF

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/11573/1436104
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact