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• W2039444018 abstract "Directed percolation is one of the generic dynamic universality classes. We study the crossover from isotropic to directed percolation by representing the combined problem as a random cluster model. A parameter $r$ controls the spontaneous birth of new forest fires. We obtain the exact crossover exponent ${y}_{mathrm{DP}}{phantom{rule{0ex}{0ex}}=phantom{rule{0ex}{0ex}}y}_{T}ensuremath{-}1$ at $rphantom{rule{0ex}{0ex}}=phantom{rule{0ex}{0ex}}1$ using Coulomb gas methods. Isotropic percolation is stable in 2D. Our numerical finite-size scaling results confirm this. An intuitive argument suggests that directed percolation at $rphantom{rule{0ex}{0ex}}=phantom{rule{0ex}{0ex}}0$ does not change stability for $Densuremath{ge}3$. It remains unstable, such that forest fires at $0<r<1$ have the same scaling properties as isotropic percolation all dimensions." @default.
• W2039444018 created "2016-06-24" @default.
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• W2039444018 creator A5043062776 @default.
• W2039444018 date "1997-03-10" @default.
• W2039444018 modified "2023-09-27" @default.
• W2039444018 title "Crossover from Isotropic to Directed Percolation" @default.
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• W2039444018 doi "https://doi.org/10.1103/physrevlett.78.1850" @default.
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