2024/07/11 by Federico Corberi, Corberi, Federico, L. A. Smaldone +1 · 1 citation
Agricultural and Biological Sciences · Medicine · #Agricultural Economics and Policy #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2407.08502
openalex publication_date 2024/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the non-equilibrium response function Rij(t,t'), namely the variation of the local magnetization ⟨ Si(t)⟩ on site i at time t as an effect of a perturbation applied at the earlier time t' on site j, in a class of solvable spin models characterized by the vanishing of the so-called \it asymmetry. This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio Xij(t,t')=βRij/(∂ Gij/∂ t'), where Gij(t,t')=⟨ Si(t)Sj(t')⟩ is the spin-spin correlation function and β is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal formXii(t,t') = (t+t')/(2t), whereas lim t→ ∞Xij(t,t')=1/2 for any ij couple. The specific case of voter models with long-range interactions is thoroughly discussed.