The paper extends the Brock-Durlauf social interactions model to richer social structures modelled with arbitrary interaction topologies and examines in detail the star, the wheel and the path. It explores Nash equilibria when agents act on the basis of expectations over, and, alternatively,...

A stochastic resonator constructed of three discrete states is proposed to explain microscopically why one applies the Arrhenius-type relaxation time to the time scale of thermal relaxation of each two-state kinetic Ising spin in previous papers which have studied stochastic resonance using...

In this paper, we consider a discrete choice model where heterogeneous agents are subject to mutual influences. We explore some consequences on the market's behaviour, in the simplest case of a uniform willingness to pay distribution. We exhibit a first-order phase transition in the profit...

We investigate a simple system of two coupled discrete stochastic resonators in the following two cases, to clarify the role of coupling. Case A: an oscillating force is applied to the whole system. Case B: an oscillating force is applied to one of the coupled resonators. We have obtained...

Using the effective field theory with a probability distribution technique that accounts for the self-spin correlations, we have studied the influence of surface defects on the critical properties of the magnetic spin Ising film. We discuss an L layer film of simple cubic symmetry with...

We use the recently developed critical minimum energy subspace (CrMES) approximation scheme to study the critical behavior of the Baxter–Wu model. This scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with...

We propose a model to simulate the process of opinion formation in a society where the traditional division into leftists and rightists is not enough any longer. The model is based on the Ashkin–Teller idea to assign two Ising spins to each site (agent). The two states (up and down) of the...