In this paper, we study the annealed ferromagnetic Ising model on the configuration model. In an annealed system, we take the average on both sides of the ratio defining the Boltzmann–Gibbs measure of the Ising model. In the configuration model, the degrees are specified. Remarkably, when the degrees are deterministic, the critical value of the annealed Ising model is the same as that for the quenched Ising model. For independent and identically distributed (i.i.d.) degrees, instead, the annealed critical value is strictly smaller than that of the quenched Ising model. This identifies the degree structure of the underlying graph as the main driver for the critical value. Furthermore, in both contexts (deterministic or random degrees), we provide the variational expression for the annealed pressure. Interestingly, our rigorous results establish that only part of the heuristic conjectures in the physics literature were correct.

Annealed Ising model on configuration models / Can, Van Hao; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - 58:1(2022), pp. 134-163. [10.1214/21-AIHP1156]

Annealed Ising model on configuration models

Giardinà, Cristian
;
Giberti, Claudio;
2022

Abstract

In this paper, we study the annealed ferromagnetic Ising model on the configuration model. In an annealed system, we take the average on both sides of the ratio defining the Boltzmann–Gibbs measure of the Ising model. In the configuration model, the degrees are specified. Remarkably, when the degrees are deterministic, the critical value of the annealed Ising model is the same as that for the quenched Ising model. For independent and identically distributed (i.i.d.) degrees, instead, the annealed critical value is strictly smaller than that of the quenched Ising model. This identifies the degree structure of the underlying graph as the main driver for the critical value. Furthermore, in both contexts (deterministic or random degrees), we provide the variational expression for the annealed pressure. Interestingly, our rigorous results establish that only part of the heuristic conjectures in the physics literature were correct.
58
1
134
163
Annealed Ising model on configuration models / Can, Van Hao; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco. - In: ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. - ISSN 0246-0203. - 58:1(2022), pp. 134-163. [10.1214/21-AIHP1156]
Can, Van Hao; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco
File in questo prodotto:
File Dimensione Formato  
AIHP1156.pdf

accesso aperto

Descrizione: Articolo
Tipologia: Versione dell'editore (versione pubblicata)
Dimensione 358.35 kB
Formato Adobe PDF
358.35 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1260579
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact