Statics and dynamics of the infinite-range Ising spin glass model

The Sherrington-Kirkpatrick (SK) spin glass model (1975) is studied by Monte Carlo simulation. Below Tc there is a spectrum of relaxation times which diverge like exp(cN14/) as N, the number of spins, tends to infinity. In zero field, h, there is one more timescale, tau eg, which is the time to turn over all the spins. Averaging over samples (ln tau eg)j(=ln tau eg) varies as N12/. However, ln tau eg is not a self-averaging quantity and there are large sample-to-sample variations even for N to infinity . For h>>h*=T/N12/, where T is the temperature, fluctuations on timescale tau eg may not occur. Above the Almeida-Thouless line (1978) relaxation times are finite and the SK solution is correct. Below this line, the results agree well with Parisi's theory (1983) if the latter is correctly interpreted.

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