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

Abstract : The long-range one-dimensional Ising spin-glass with random couplings decaying as J(r) ∝ r −σ presents a spin-glass phase Tc(σ) > 0 for 0 ≤ σ < 1 (the limit σ = 0 corresponds to the mean-field SK-model). We use the eigenvalue method introduced in our previous work [C. Monthus and T. Garel, J. Stat. Mech. P12017 (2009)] to measure the equilibrium time teq(N) at temperature T = Tc(σ)/2 as a function of the number N of spins. We find the activated scaling ln teq(N) ∼ N ψ with the same barrier exponent ψ ≃ 0.33 in the whole region 0 ≤ σ < 1.
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Cécile Monthus, Thomas Garel. Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass. Biophysical Reviews and Letters, World Scientific Publishing, 2014, 89, pp.014408 ⟨10.1103/PhysRevB.89.014408⟩. ⟨cea-01323412⟩

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