2004/10/31 by Federico Corberi, Eugenio Lippiello, Marco Zannetti
Mathematics · Physics and Astronomy · #Biology #Complex Network Analysis Techniques #Function (biology) #Geometry #Ising model #Kinetic energy #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.056103
published as Phys. Rev. E 72, 056103 (2005) · 16 pages, 11 figures. Thoroughly revised version. New figures. To be published in Phys.Rev.E
arxiv created 2005/09/19 · openalex publication_date 2005/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The aging part Rag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form Rag(t,s)=s-(1+a)f(t/s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273+/-0.006, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function f(t/s) and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for Rag(t,s). This gives a satisfactory qualitative agreement with the numerical data for Rag(t,s) and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in Rag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties.