We study the non-equilibrium response function R i j ( t , t ′ ) , namely the variation of the local magnetization ⟨ S i ( 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 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 X i j ( t , t ′ ) = β R i j / ( ∂ G i j / ∂ t ′ ) , where G i j ( t , t ′ ) = ⟨ S i ( t ) S j ( 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 form X i i ( t , t ′ ) = ( t + t ′ ) / ( 2 t ) , whereas lim t → ∞ X i j ( t , t ′ ) = 1 / 2 for any ij couple. The specific case of voter models with long-range interactions is thoroughly discussed.

General properties of the response function in a class of solvable non-equilibrium models

Corberi F.
Writing – Original Draft Preparation
;
Smaldone L.
Writing – Original Draft Preparation
2024-01-01

Abstract

We study the non-equilibrium response function R i j ( t , t ′ ) , namely the variation of the local magnetization ⟨ S i ( 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 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 X i j ( t , t ′ ) = β R i j / ( ∂ G i j / ∂ t ′ ) , where G i j ( t , t ′ ) = ⟨ S i ( t ) S j ( 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 form X i i ( t , t ′ ) = ( t + t ′ ) / ( 2 t ) , whereas lim t → ∞ X i j ( t , t ′ ) = 1 / 2 for any ij couple. The specific case of voter models with long-range interactions is thoroughly discussed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4887447
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