Nuno Crokidakis, Paulo Murilo Castro de Oliveira
In this work we study a modified version of the majority-vote model with noise. In particular, we consider a random diluted square lattice for which a site is empty with a probability $r$. In order to analyze the critical behavior of the model, we perform Monte Carlo simulations on lattices with linear sizes up to L=140. By means of a finite-size scaling analysis we estimate the critical noises $q_{c}$ and the critical ratios $\beta/\nu$, $\gamma/\nu$ and $1/\nu$ for some values of the probability $r$. Our results suggest that the critical exponents are different from those of the original model ($r=0$), but they are $r$-independent ($r>0$). In addition, if we consider that agents can diffuse through the lattice, the exponents remain the same, which suggests a new universality class for the majority-vote model with noise. Based on the numerical data, we may conjecture that the values of the exponents in this universality class are $\beta\sim 0.45$, $\gamma\sim 1.1$ and $\nu\sim 1.0$, which satisfy the scaling relation $2\beta+\gamma=d\,\nu=2$.
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http://arxiv.org/abs/1204.3885
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