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Register a new userRelaxational dynamics in 3D randomly diluted Ising models
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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).
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We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.
The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma.
We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.
By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and system size, we find that the paramagnetic phase covers the entire T>0 range. Our results enable us to obtain an estimate of the critical exponent associated to the correlation length at T=0, 1/nu=0.35(10).
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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