[en] Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdoes-Renyi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the noise critical q_c to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies cited above giving the same behavior regardless of dynamic or topology used here.

[en] A brief review is given on the study of the thermodynamic properties of spin models defined on different topologies like small-world, scale-free networks, random graphs and regular and random lattices. Ising, Potts and Blume-Capel models are considered. They are defined on complex lattices comprising Appolonian, Barabási-Albert, Voronoi-Delauny and small-world networks. The main emphasis is given on the corresponding phase transitions, transition temperatures, critical exponents and universality, compared to those obtained by the same models on regular Bravais lattices

[en] The critical properties of the Potts model with $q=3$ and 8 states in one-dimension on directed small-world networks are investigated. This disordered system is simulated by updating it with the Monte Carlo heat bath algorithm. The Potts model on these directed small-world networks presents in fact a second-order phase transition with a new set of critical exponents for $q=3$ considering a rewiring probability $p=0.1$. For $q=8$ the system exhibits only a first-order phase transition independent of p.

[en] We investigated majority vote model coupled with quasiperiodic tilings by using both Monte Carlo and finite size scaling techniques. We obtained numerically the following averages: Binder cumulant , order parameter , defined as the averaged opinion balance, and its respective susceptibility . Our numerical results suggest that the system falls in two-dimensional Ising universality class. In addition, our results are in agreement with Harris–Barghathi–Vojta criterion, which states that two-dimensional quasiperiodic ordering is irrelevant and does not change any of the critical exponents. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] We consider the Biswas–Chatterjee–Sen model on Barabasi–Albert networks. This system undergoes a continuous phase transition from a consensus state to a disordered state by increasing a noise parameter q over a critical threshold q _c. The noise parameter is defined as the probability of the affinity between two neighbors being negative, modeling Galam contrarians. We obtained the critical exponent ratios , , and by finite-size scaling data collapses, as well as the critical noises. Our numerical data is consistent with the critical thresholds q _c being a linear function of the inverse of network connectivity z, and with an asymptotic value of q _c  =  0.3418, close to the value of the critical noise for the complete graph. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time t _max, exponentially distributed with mean inversely proportional to the node population in order to model the individuals’ interactions. Our simulation results of the modified model on Barabasi–Albert networks are compatible with a continuous absorbing-active phase transition when increasing the average concentration. The transition obeys the mean-field critical exponents β = 1, γ′ = 0 and ν _⊥ = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents $\stackrel{^<!--\; ^\; -->}{\mathrm{\beta <!--\; ??\; -->}}={\stackrel{^<!--\; ^\; -->}{\mathrm{\gamma <!--\; ??\; -->}}}^{\mathrm{\prime <!--\; ???\; -->}}=-<!--\; ???\; -->3/2$ on the order parameter and its fluctuations, respectively. The most evident implication of our simulation results is if the individuals avoid social interactions in order to not spread a disease, this leads the system to have a finite threshold in scale-free graphs. (paper)