Scaling and persistence in the two-dimensional Ising model
- 17 November 2000
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (47) , 8383-8388
- https://doi.org/10.1088/0305-4470/33/47/305
Abstract
The spatial distribution of persistent spins at zero temperature in the pure two-dimensional Ising model is investigated numerically. A persistence correlation length, ξ(t)~tZ, is identified such that for length scales r<<ξ(t) the persistent spins form a fractal with dimension df; for length scales r>>ξ(t) the distribution of persistent spins is homogeneous. The zero-temperature persistence exponent, θ, is found to satisfy the scaling relation θ = Z(2-df) with θ = 0.209±0.002 of Jain (Jain S 1999 Phys. Rev. E 59 R2493), Z = 1/2 and df~1.58.Keywords
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This publication has 10 references indexed in Scilit:
- Scaling and fractal formation in persistenceJournal of Physics A: General Physics, 2000
- Zero-temperature dynamics of the weakly disordered Ising modelPhysical Review E, 1999
- Persistence with Partial SurvivalPhysical Review Letters, 1998
- Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts modelJournal of Statistical Physics, 1996
- Persistent Spins in the Linear Diffusion Approximation of Phase Ordering and Zeros of Stationary Gaussian ProcessesPhysical Review Letters, 1996
- Nontrivial Exponent for Simple DiffusionPhysical Review Letters, 1996
- Exact First-Passage Exponents of 1D Domain Growth: Relation to a Reaction-Diffusion ModelPhysical Review Letters, 1995
- Ising spinodal decomposition at T=O in one to five dimensionsJournal of Physics A: General Physics, 1994
- Non-Trivial Algebraic Decay in a Soluble Model of CoarseningEurophysics Letters, 1994
- Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts modelsJournal of Physics A: General Physics, 1994