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Center for Nonlinear Studies |
We discuss a meta-heuristic method based on self-organized criticality. While the heuristic is applicable to many NP-hard combinatorial problems, we present here simulations on very large, frustrated spin systems with quenched disorder in the glassy state. Specifically, results are presented for low-temperature excitations of the bond-diluted Edwards-Anderson spin glass. Well above bond percolation $p_c$, dilution provides an efficient means to obtain accurate predictions for equilibrium properties of the glassy phase. The domain-wall stiffness exponent $y_d$ is computed in up to $d=7$ dimensions. Fitting $y_d$ yields a lower critical dimension of $d_l=5/2$ (where $y_d=0$) to within 0.1\%, in agreement with replica theory. Directly at $p_c$, the boundary between the spin-glass and the paramagnetic phase at $T=0$, equilibrium theory provides experimentally testable predictions for the shape of the phase boundary $T_g\sim(p-p_c)^\phi$, with simulations predicting $\phi=1.12(1)$.
Host: Carl Bender, T-CNLS