Massimo Ostilli

Statistical mechanics of rumour spreading in network communities

We report a preliminary investigation on interactions between networked social communities using the Ising model to analyze the spread of rumours. The inner opinion of a given community is forced to change through the introduction of a unique external source and we analyze how the other communities react to this change. We model two conceptual external sources: namely, “Strong-belief ”, and “Propaganda”, by an infinitely strong inhomogeneous external field and a finite uniform external field, respectively. In the former case, the community changes independently from other communities while in the latter case according also to interactions with the other communities. We apply our model to synthetic networks as well as various real world data ranging from human physical contact networks to online social networks. The experimental results using real world data clearly demonstrate two distinct scenarios of phase transitions.

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.

Small-world of communities: communication and correlation of the meta-network

The long-time behaviors of the velocity autocorrelation function

Ising spin glass models versus Ising models: an effective mapping at high temperature: I. General result

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Fluctuation analysis in complex networks modeled by hidden-variable models: necessity of a large cutoff in hidden-variable models.

for sheared fluids ^M are investigated theoretically and numerically. It is found the existence of the cross-overs of^M

Duality between equilibrium and growing networks.

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Critical behavior and correlations on scale-free small-world networks: application to network design.

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First- and second-order phase transitions in Ising models on small-world networks: Simulations and comparison with an effective field theory

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Effective field theory for models defined over small-world networks: first- and second-order phase transitions.

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Ising spin glass models versus Ising models: an effective mapping at high temperature: II. Applications to graphs and networks

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