In this work we study a modified version of the Sznajd sociophysics model. In particular we introduce reputation, a mechanism that limits the capacity of persuasion of the agents. The reputation is introduced as a score which is time-dependent, and its introduction avoid dictatorship (all spins parallel) for a wide range of parameters. The relaxation time follows a log-normal-like distribution. In addition, we show that the usual phase transition also occurs, as in the standard model, and it depends on the initial concentration of individuals following an opinion, occurring at a initial density of up spins greater than $1/2$. The transition point is determined by means of a finite-size scaling analysis.Comment: 8 pages, 4 figures, To be published in Physics Letters

We study the surface growth generated by the random deposition of particles of different sizes. A model is proposed where the particles are aggregated on an initially flat surface, giving rise to a rough interface and a porous bulk. By using Monte Carlo simulations, a surface has grown by adding particles of different sizes, as well as identical particles on the substrate in (1 + 1) dimensions. In the case of deposition of particles of different sizes, they are selected from a Poisson distribution, where the particle's sizes may vary by one order of magnitude. For the deposition of identical particles, only particles which are larger than one lattice parameter of the substrate are considered. We calculate the usual scaling exponents: the roughness, growth and dynamic exponents α, β and z, respectively, as well as, the porosity in the bulk, determining the porosity as a function of the particle size. The results of our simulations show that the roughness evolves in time following three different behaviors. The roughness in the initial times behaves as in the random deposition model. At intermediate times, the surface roughness grows slowly and finally, at long times, it enters into the saturation regime. The bulk formed by depositing large particles reveals a porosity that increases very fast at the initial times, and also reaches a saturation value. Excepting the case where particles have the size of one lattice spacing, we always find that the surface roughness and porosity reach limiting values at long times. Surprisingly, we find that the scaling exponents are the same as those predicted by the Villain-Lai-Das Sarma equation.

We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation-a mechanism limiting the agents' persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents' reputation increases for each persuaded neighbor, and case 2, in which the agents' reputation increases for each persuasion and decreases when a neighbor keeps his opinion. Our results show that the introduction of reputation avoids full consensus even for initial densities of up spins greater than 1/2. The relaxation times follow a log-normal-like distribution in both cases, but they are larger in case 2 due to the competition among reputations. In addition, we show that the usual phase transition occurs and depends on the initial concentration d of individuals with the same opinion, but the critical points d c in the two cases are different.