Scaling and persistence in the two-dimensional Ising model

S. Jain*, H. Flynn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)8383-8388
Number of pages6
JournalJournal of Physics A: Mathematical and General
Issue number47
Publication statusPublished - 1 Dec 2000

Bibliographical note

Funding: University of Derby research studentship.


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