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Register a new userEntropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings
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We study link-diluted $pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.
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Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to study dynamic heterogeneities and the presence of a replicon mode and to obtain safe bounds on the Edwards-Anderson order parameter below the critical temperature. We obtain good agreement with experimental determinations of the temperature-dependent decay exponents for the thermoremanent magnetization. This magnitude is observed to scale with the much harder to measure coherence length, a potentially useful result for experimentalists. The exponents for energy relaxation display a linear dependence on temperature and reasonable extrapolations to the critical point. We conclude examining the time growth of the coherence length, with a comparison of critical and activated dynamics.
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 present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.
We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear second order differential equation that depends on a diffusion-like parameter D. We apply it to the problem of finding ground states of 2d Ising spin glasses for the +-J-Model. We consider square lattices with side length up to L=24 with two different types of boundary conditions and compare the results to those obtained by exact methods. A particular value of D is found that yields an optimal performance of the algorithm. We compare this optimal value of D to a percolation transition, which occurs when studying the connected clusters of spins flipped by the algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has more and more problems to find the exact ground states. This means that the approach, at least in its standard form, seems to be inferior to other approaches like parallel tempering.
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