Simulations find that the inverse energy gap in 2D Edwards-Anderson spin glasses develops a fat-tailed distribution with infinite variance for large N, while the Sherrington-Kirkpatrick model shows a finite-variance gap scaling roughly as N to the power -1/3.
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Energy gap of quantum spin glasses: a projection quantum Monte Carlo study
Simulations find that the inverse energy gap in 2D Edwards-Anderson spin glasses develops a fat-tailed distribution with infinite variance for large N, while the Sherrington-Kirkpatrick model shows a finite-variance gap scaling roughly as N to the power -1/3.