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Physical Review Letters

Emergence of Fast Local Dynamics on Cooling toward the Ising Spin Glass Transition

Peter H. Poole, Sharon C. Glotzer, Antonio Coniglio A, Naeem Jan

Published Apr 28, 1997• 32 citations
Publisher

Abstract

We present a detailed Monte Carlo evaluation of the equilibrium distribution of local spin-flip rates and local energies in the paramagnetic phase of the $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ and $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ifmmode\pm\else\textpm\fi{}J$ Ising spin glass. Both quantities are spatially heterogeneous, and we find that the shapes of the distributions change dramatically with decreasing temperature. In particular as temperature decreases we find that for an increasing fraction of spins the local spin-flip rate and local energy increase as the glass transition is approached.

DOI
10.1103/physrevlett.78.3394

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Critical behavior of three-dimensional Ising spin-glass model

Andrew T. Ogielski, I. Morgenstern

First results of massive Monte Carlo simulations of the d=3 Ising spin-glass with \ifmmode\pm\else\textpm\fi{}J bond distribution, performed on a fast special purpose computer, are presented. A qualitative change in the behavior of the system and best fits for the spin-glass correlation length and relaxation time favor equilibrium phase transition at ${\mathrm{T}}_{\mathrm{c}}$/J\ensuremath{\approxeq}1.2. .AE

Physical Review Letters•Mar 4, 1985•362 citations
We present a detailed Monte Carlo evaluation of the equilibrium distribution of local spin-flip rates and local energies in the paramagnetic phase of the d=2d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2d=2 and d=3\ifmmode±\else\textpm\fiJd\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ifmmode\pm\else\textpm\fi{}Jd=3\ifmmode±\else\textpm\fiJ Ising spin glass. Both quantities are spatially heterogeneous, and we find that the shapes of the distributions change dramatically with decreasing temperature. In particular as temperature decreases we find that for an increasing fraction of spins the local spin-flip rate and local energy increase as the glass transition is approached.
We have performed a detailed analysis of the local dynamics and local energies of the equilibrium, paramagnetic phase of the d = 2 and d = 3 ±J Ising spin glass model. Here we discuss our recently reported observations1) that while the average flip rate and average energy decrease monotonically with decreasing temperature, both the flip rate and energy of an increasing fraction of spins increase as the glass transition is approached on cooling. These findings are consistent with recent experimental results for the frequency-dependent magnetic susceptibility of an insulating spin glass, which showed that the approach to the glass transition could be detected from the high frequency behavior.
We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.
By using frustration-preserving hard-spin mean-field theory, we investigated the phase-transition dynamics in the three-dimensional field-free ± J Ising spin-glass model. As the temperature T is decreased from paramagnetic phase at high temperatures, with a rate ω=-dT/dt in time t, the critical temperature depends on the cooling rate through a clear power law ω^{a}. With increasing antiferromagnetic bond fraction p, the exponent a increases for the transition into the ferromagnetic case for p<p_{c} and decreases for the transition into the spin-glass phase for p>p_{c}, signaling the ferromagnetic - spin-glass phase transition at p_{c}≈0.22. The relaxation time is also investigated in the adiabatic case ω=0 and the dynamic exponent zν is found to increase with increasing p.
First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.
First results of massive Monte Carlo simulations of the d=3 Ising spin-glass with \ifmmode\pm\else\textpm\fi{}J bond distribution, performed on a fast special purpose computer, are presented. A qualitative change in the behavior of the system and best fits for the spin-glass correlation length and relaxation time favor equilibrium phase transition at Tc{\mathrm{T}}_{\mathrm{c}}Tc​/J\ensuremath{\approxeq}1.2. .AE