Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

Helmut G. Katzgraber and A.P. Young
Phys. Rev. B 67, 134410 (2003), cond-mat/0210451.

Abstract
We present results from Monte Carlo simulations of the one-dimensional Ising spin glass with power-law interactions at low temperature, using the parallel tempering Monte Carlo method. For a set of parameters where the long-range part of the interaction is relevant, we find evidence for large-scale droplet-like excitations with an energy that is independent of system size, consistent with replica symmetry breaking. We also perform zero-temperature defect energy calculations for a range of parameters and find a stiffness exponent for domain walls in reasonable, but by no means perfect agreement with analytic predictions

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