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Register a new userEvidence of many thermodynamic states of the three-dimensional Ising spin glass
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We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our state-of-the-art simulation and variance reduction data analysis suggest that the many pure state picture is most likely and coherent.
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The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, u = 2.562(42) for the thermal exponent, eta = -0.3900(36) for the anomalous dimension and omega = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield alpha = -5.69(13), beta = 0.782(10) and gamma = 6.13(11). We also compute several universal quantities at Tc.
We study the XY spin glass by large-scale Monte Carlo simulations for sizes up to 24^3, down to temperatures below the transition temperature found in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes indicating that the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a very similar manner. We also address the optimal ratio of over-relaxation to Metropolis sweeps in the simulation.
We use a non-equilibrium simulation method to study the spin glass 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. The normally problematic critical slowing-down is not hampering this kind of approach, since the system equilibrates quickly at the initial temperature and the slowing-down is merely reflected in the dynamic scaling of the non-equilibrium order parameter with $v$ and the system size. The equilibrium limit does not have to be reached. For the dynamic exponent we obtain $z = 5.85(9)$ for bimodal couplings distribution and $z=6.00(10)$ for the Gaussian case, thus supporting universal dynamic scaling (in contrast to recent claims of non-universal behavior).
We perform numerical simulations, including parallel tempering, on the Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the location of the transition and the value of the critical exponents. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the random permutation Potts glass.
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