Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin glass

2013/09/30 by Cécile Monthus, Cecile Monthus, Thomas Garel · 11 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Exponent #Ising model #Ising spin #Materials science #Mathematical physics #Mathematics #Measure (data warehouse) #Physics #Quantum mechanics #Range (aeronautics) #Scaling #Sigma #Spin (aerodynamics) #Spin glass #Spins #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevb.89.014408

published in Physical Review B 89(1) (American Physical Society) · v3=final version (12 pages)

openalex publication_date 2014/01/09 · arxiv created 2014/01/10 · arxiv updated 2014/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The long-range one-dimensional Ising spin glass with random couplings decaying as J(r)\ensuremath∝r^\ensuremath-\ensuremathσ presents a spin-glass phase T_c(\ensuremathσ)>0 for 0\ensuremath≤\ensuremathσ<1 (the limit \ensuremathσ=0 corresponds to the mean-field Sherrington-Kirkpatrick model). We use the eigenvalue method introduced in our previous work (C. Monthus and T. Garel, J. Stat. Mech. 2009, P12017) to measure the equilibrium time t_eq(N) at temperature T=T_c(\ensuremathσ)/2 as a function of the number N of spins. We find the activated scaling lnt_eq(N)\ensuremath∼N^\ensuremathψ with the same barrier exponent \ensuremathψ\ensuremath≃0.33 in the whole region 0\ensuremath≤\ensuremathσ<1.

Citations

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