The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance

TL;DR

This paper investigates the non-equilibrium response of the 2D critical Ising model, revealing discrepancies with Local Scale Invariance predictions and highlighting the limits of its applicability in describing scaling behavior.

Contribution

The study provides Monte Carlo simulation evidence showing that Local Scale Invariance does not fully capture the response function scaling in the critical Ising model.

Findings

Discrepancies between actual and predicted scaling behaviors.

Impulse autoresponse function shows clear deviations.

Integrated response functions align more closely with predictions.

Abstract

Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al., we detect discrepancies between the actual scaling behavior of the response function and the prediction of Local Scale Invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in integrated response functions. Accordingly, the scaling form predicted on the basis of Local Scale Invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.