We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other individuals in the network. To model such dynamics, we consider the Ising model with an external magnetic field on a family of finite networks with a clustered structure. Assuming a unit strength for the interactions inside each community, we assume that the strength of interaction across different communities is described by a scalar $\epsilon \in [-1,1]$, which allows a weaker but possibly antagonistic effect between communities. We are interested in the stochastic evolution of this system described by a Glauber-type dynamics parameterized by the inverse temperature $\beta$. We focus on the low-temperature regime $\beta\rightarrow\infty$, in which homogeneous opinion patterns prevail and, as such, it takes the network a long time to fully change opinion. We investigate the different metastable and stable states of this opinion dynamics model and how they depend on the values of the parameters $\epsilon$ and $h$. More precisely, using tools from statistical physics, we derive rigorous estimates in probability, expectation, and law for the first hitting time between metastable (or stable) states and (other) stable states, together with tight bounds on the mixing time and spectral gap of the Markov chain describing the network dynamics. Lastly, we provide a full characterization of the critical configurations for the dynamics, i.e., those which are visited with high probability along the transitions of interest.

Ising model on clustered networks: A model for opinion dynamics / Simone Baldassarri; Anna Gallo; Vanessa Jacquier; Alessandro Zocca. - In: PHYSICA. A. - ISSN 0378-4371. - ELETTRONICO. - 623:(2023), pp. 1-25. [10.1016/j.physa.2023.128811]

Ising model on clustered networks: A model for opinion dynamics

Simone Baldassarri
Membro del Collaboration Group
;
Vanessa Jacquier
Membro del Collaboration Group
;
2023

Abstract

We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other individuals in the network. To model such dynamics, we consider the Ising model with an external magnetic field on a family of finite networks with a clustered structure. Assuming a unit strength for the interactions inside each community, we assume that the strength of interaction across different communities is described by a scalar $\epsilon \in [-1,1]$, which allows a weaker but possibly antagonistic effect between communities. We are interested in the stochastic evolution of this system described by a Glauber-type dynamics parameterized by the inverse temperature $\beta$. We focus on the low-temperature regime $\beta\rightarrow\infty$, in which homogeneous opinion patterns prevail and, as such, it takes the network a long time to fully change opinion. We investigate the different metastable and stable states of this opinion dynamics model and how they depend on the values of the parameters $\epsilon$ and $h$. More precisely, using tools from statistical physics, we derive rigorous estimates in probability, expectation, and law for the first hitting time between metastable (or stable) states and (other) stable states, together with tight bounds on the mixing time and spectral gap of the Markov chain describing the network dynamics. Lastly, we provide a full characterization of the critical configurations for the dynamics, i.e., those which are visited with high probability along the transitions of interest.
2023
623
1
25
Simone Baldassarri; Anna Gallo; Vanessa Jacquier; Alessandro Zocca
File in questo prodotto:
File Dimensione Formato  
preprintBGJZ.pdf

accesso aperto

Descrizione: PreprintBGJZ
Tipologia: Pdf editoriale (Version of record)
Licenza: Open Access
Dimensione 1.04 MB
Formato Adobe PDF
1.04 MB Adobe PDF
Ising model on clustered graphs.pdf

accesso aperto

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Open Access
Dimensione 1.12 MB
Formato Adobe PDF
1.12 MB Adobe PDF

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

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1295141
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact