We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we use the Adaptive Cluster Expansion method [S. Cocco, R. Monasson, Phys. Rev. Lett. 106, 090601 (2011)], originally developed to solve the inverse Ising problem, that is, to infer the interactions from the equilibrium correlations. The method consists in iteratively constructing and selecting clusters of spins, computing their contributions to the free energy and discarding clusters whose contribution is lower than a fixed threshold. The properties of the cluster expansion and its performance are studied in detail on one dimensional, two dimensional, random and fully connected graphs with homogeneous or heterogeneous fields and couplings. We discuss the differences between different representations (Boolean and Ising) of the spin variables.

Adaptive cluster expansion for Ising spin models / Cocco, S; Croce, G; Zamponi, F. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - 92:11(2019). [10.1140/epjb/e2019-100313-9]

Adaptive cluster expansion for Ising spin models

Zamponi F
2019

Abstract

We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we use the Adaptive Cluster Expansion method [S. Cocco, R. Monasson, Phys. Rev. Lett. 106, 090601 (2011)], originally developed to solve the inverse Ising problem, that is, to infer the interactions from the equilibrium correlations. The method consists in iteratively constructing and selecting clusters of spins, computing their contributions to the free energy and discarding clusters whose contribution is lower than a fixed threshold. The properties of the cluster expansion and its performance are studied in detail on one dimensional, two dimensional, random and fully connected graphs with homogeneous or heterogeneous fields and couplings. We discuss the differences between different representations (Boolean and Ising) of the spin variables.
2019
Optimization problems; satisfiability; message passing
01 Pubblicazione su rivista::01a Articolo in rivista
Adaptive cluster expansion for Ising spin models / Cocco, S; Croce, G; Zamponi, F. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - 92:11(2019). [10.1140/epjb/e2019-100313-9]
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/11573/1693803
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact