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Register a new userOn the random neighbor Olami-Feder-Christensen slip-stick model
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Added by
Carmen P. C. do Prado
Publication date
1998
fields
Physics
and research's language is
English
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We reconsider the treatment of Lise and Jensen (Phys. Rev. Lett. 76, 2326 (1996)) on the random neighbor Olami-Feder-Christensen stik-slip model, and examine the strong dependence of the results on the approximations used for the distribution of states p(E).
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A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this distribution function with the lattice size is usually enough to assume that any cut off will disappear as the lattice size goes to infinity. This approach, however, can lead to misleading conclusions. In this work we analyze the behavior of the branching rate sigma of the events to establish whether a system is in a critical state. We apply this method to the Olami-Feder-Christensen model to obtain evidences that, in contrast to previous results, the model is critical in the conservative regime only.
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We report some numerical simulations to investigate the existence of a self-organized critical (SOC) state in a random-neighbor version of the OFC model for a range of parameters corresponding to a non-conservative case. In contrast to a recent work, we do not find any evidence of SOC. We use a more realistic distribution of energy among sites to perform some analytical calculations that agree with our numerical conclusions.
The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents $gamma$ and $beta$ are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be $q_{c}=0.117pm0.005$.
We present a complementary estimation of the critical exponent $alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $alpha = 0.12(2)$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$.
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