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ABSTRACT: We present in detail the scaling analysis and data collapse of avalanche distributions and joint distributions that characterize the recently evidenced critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model. The distributions are collected in extensive simulations of systems with linear sizes up to L=131072.
Physical Review E 11/2011; 84(5 Pt 1):051119. · 2.26 Impact Factor
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ABSTRACT: We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.
Physical Review Letters 04/2011; 106(17):175701. · 7.37 Impact Factor
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ABSTRACT: We study the statistics of equally weighted random walk paths on a family of Sierpinski gasket lattices whose members are labelled by an integer b (2 ≤ b < ∞). The obtained exact results on the first eight members of this family reveal that, for every b > 2, mean path end-to-end distance grows more slowly than any power of its length N. We provide arguments for the emergence of usual power law critical behaviour in the limit b → ∞ when fractal lattices become almost compact.
Journal of Physics A General Physics 12/2003; 37(1):1.
