1998/11/13 by Iaroslav Ispolatov, Yaroslav Ispolatov
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.60.r2437
4 pages 4 figures
arxiv created 1998/11/13 · openalex publication_date 1999/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Persistence in coarsening one-dimensional spin systems with a power-law interaction r^\ensuremath-1\ensuremath-\ensuremathσ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent \ensuremathσ (\ensuremathσ>~1/2 in our simulations), persistence decays as an algebraic function of the length scale L, P(L)\ensuremath∼L^\ensuremath-\ensuremathθ. The persistence exponent \ensuremathθ is found to be independent on the force exponent \ensuremathσ and close to its value for the extremal (\stackrel\ensuremath→\ensuremathσ\ensuremath∞) model, \ensuremathθ=0.17507588\ensuremath⋅\ensuremath⋅\ensuremath⋅. For smaller values of the force exponent (\ensuremathσ<1/2), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small \ensuremathσ, the system size should grow as [O(1/\ensuremathσ)]^1/\ensuremathσ.