Numerical study of the dynamics of some long range spin glass models

Abstract

We present results of a Monte Carlo study of the equilibrium dynamics of the one dimensional long-range Ising spin glass model. By tuning a parameter $\sigma$, this model interpolates between the mean field Sherrington-Kirkpatrick model and a proxy of the finite dimensional Edward-Anderson model. Activated scaling fits for the behavior of the relaxation time $\tau$ as a function of the number of spins $N$ (Namely $\ln (\tau )\propto N^{\psi }$) give values of $\psi$ that are not stable against inclusion of subleading corrections. Critical scaling ($\tau \propto N^{\rho }$) gives more stable fits, at least in the non mean field region. We also present results on the scaling of the time decay of the critical remanent magnetization of the Sherrington-Kirkpatrick model, a case where the simulation can be done with quite large systems and that shows the difficulties in obtaining precise values for dynamical exponents in spin glass models.

References in corpus (7)

• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• The correspondence between long-range and short-range spin glasses
• Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
• Critical Off-Equilibrium Dynamics in Glassy Systems
• Distribution of time scales in the Sherrington-Kirkpatrick model

Cited by in corpus (1)

• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization