Harnessing finite-size effects to gauge aging in the 2D Ising model

2026/07/31 by Dustin Warkotsch, Malte Henkel, Wolfhard Janke
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1088/1742-5468/ae8439

published as Dustin Warkotsch et al J. Stat. Mech. (2026) 073208 · 18 pages, 16 figures; changes: minor grammar revisions, inclusion of lambda^* estimates in text, hyperlinks of ISBNs to DOIs, minor corrections in Refs

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

The relaxation behavior towards equilibrium of the 2D Ising model with nearest-neighbor interactions has been studied with focus on the two-time autocorrelator C(t,s). Finite-size effects affecting the growing magnetic domains lead to the saturation of C(t,s) with a distinct plateau of height C_∞⁽²⁾(s,L) scaling algebraically with waiting time s and lattice size L. These scaling relations are used to produce precise estimates for the autocorrelation exponent λ and dynamical exponent z with deliberately small lattices. Treating smooth domain walls in a similar manner to the lattice boundaries, their effect on C(t,s) can be understood as premature finite-size phenomenon, extending our ansatz to systems not yet in equilibrium.

Citations

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