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- W1991027096 abstract "Abstract The directed Abelian sandpile models are defined on a square lattice by introducing a parameter, c , representing the degree of anisotropy in the avalanche processes, in which c =1 is for the isotropic case. We calculate the expected number of the topplings per added particle, 〈 T 〉, which depends on the lattice size L as L x for large L . Our exact solution gives that x =1 when any anisotropy is included in the system, while x =2 in the isotropic case. These results allow us to introduce a new critical exponent, θ , defined by χ ≡lim L →∞ 〈 T 〉/ L with c ≠1 as χ ∼| c −1| − θ for | c −1|⪡1. From the explicit expression of 〈 T 〉, we obtain θ =1." @default.
- W1991027096 created "2016-06-24" @default.
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- W1991027096 date "1999-04-01" @default.
- W1991027096 modified "2023-09-27" @default.
- W1991027096 title "Effect of anisotropy on the self-organized critical states of Abelian sandpile models" @default.
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- W1991027096 doi "https://doi.org/10.1016/s0378-4371(98)00616-5" @default.
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