Narrow Results

In the four-dimensional Edwards–Anderson ±J spin glasses, we observe that the quenched energies distribution from T=2.5 are similar to those observed for the equilibrium states at T=1.0. We show that although these states appear close there are subtle differences which are only seen when we try to quench the system from T=2.5 for a longer number of Monte Carlo steps. The T=2.5 states do not evolve to those seen for the states quenched from T=1.0. We try to identify regions responsible for the subtle differences.

We introduce a new Monte Carlo algorithm which incorporates a guiding function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. Two more ingredients, namely, the elimination of irrelevant degrees of freedom and the concept of optimal temperature are also introduced which can further speed up the search process. We use this algorithm to search for the optimal path of the traveling salesman problem and the ground state energy of the Anderson–Edwards spin glass model and demonstrate that its performance is comparable with more elaborate and heuristic methods.

In this research, we have presented the phase space of the so-called spin glass or glassy systems with a one-dimensional randomly-oriented diode network (RODN) in which the bonds between the lattice points are represented with diodes and these diodes are assumed to be fully conducting in the forward biased direction, whereas they are assumed to have some constraints, in the reverse direction, depending on the temperature and/or some other external effects. Thus, a particle's conduction (or transition) probability in the reverse direction through a diode like bond, p_r, can be assumed to have values between zero and one. By employing the Monte Carlo simulation technique to the diffusion of particles through this network we have explored the relaxation mechanism, and their functional forms. Our simulation data indicates that for reverse transition probability values of p_r=1.0 and 0.9, the time dependence of the relaxation data is exponential, on the other hand for p_r<0.2 it may be represented by either power or logarithmic time dependence. However, in general, our data can be represented by a stretched exponential time dependence, exp(-(t/τ)^α), especially in the limit of long t. Here the exponent α has values in the range of 0.3≤α≤1. For α≈1, obviously, exponential time dependence is regained. The value of α≈0.3, obtained for p_r→0, is very interesting, since it is almost the same as the critical exponent, 1/3, reported in the literature for the lowest occupation probability of site points spanning percolation clusters.

In this work, the Hopfield neural network model with infinite-range interactions is simulated by using the multicanonical algorithm. All simulations and measurements are done in spin glass states of the model with discrete ± 1 values of the random variables. Physical quantities such as the energy density, the ground-state entropy and the order parameters are evaluated at all temperatures. Our results in the spin glass region show multiple degenerate ground-states and good agreement with the replica symmetry mean field solutions.

A long-standing issue in a three-dimensional Ising spin glass (3DISG) is to settle the critical exponents. Numerical simulations and a conventional finite-size-scaling analysis have given controversial estimates, in particular, for the value of thermal exponent ν. Here a recently proposed extended scaling scheme is reviewed and illustrated for the canonical two-dimensional Ising ferromagnet. By applying the extended scaling to our extensive Monte Carlo data for 3DISG, consistent estimates of critical parameters are obtained in contrast to previous analyses.

Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions:

(i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and

(ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.

The vectorized Monte Carlo algorithm by multi-spin coding is extended to the ±J Ising spin glass model on a simple cubic lattice in a magnetic field. Explicit logical expression is given for this algorithm. In addition, shorter logical expressions are found in some special cases.

They are given for the heat-bath method under the general condition and for the Metropolis method under the condition, H = 0.

In this paper an Ising model on a random lattice with strongly asymmetric couplings inspired by neural networks is studied. We investigate the phase space structure and find evidence for an ultrametric, "multivalley" structure as observed in disordered magnetic systems. We have calculated the size of the basins of attraction.

Using a simple master-slave parallelization scheme given by A. Berengoltz and J. Adler, we observe superlinear speedups during the search algorithm for the ground state energy of the ±J spin glass via biologically motivated methods. With this parallel implementation we are able to improve earlier sequentially-calculated estimates for the infinite lattice ground state energy of the square and simple cubic lattice to −1.401±0.001 and −1.787±0.003, respectively.

We make a hybrid Monte Carlo spin dynamics simulation of a dilute system of the classical Heisenberg spins coupled via the Ruderman-Kittel-Kasuya-Yoshida interaction in a wide range of spin concentration x. We find the critical concentration of the ferromagnetism x_c ~0.15. For x < x_c, the data predict the spin glass phase transition at a finite temperature T_g. For x ≳ x_c, those predict the reentrance to a mixed phase of the ferromagnetism and a transverse spin glass at a low temperature T_m. The obtained phase diagram is seen to be quite similar to those of dilute alloys Au_{1 − x}Fe_x and Pt_{1 − x}Mn_x.

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulation results not only in isothermal aging but also in T-shift aging process. T-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.

A heuristic optimization algorithm is developed based on the renormalization group idea and applied to the Edwards–Anderson model in two dimensions with symmetric Gaussian bond distribution. Droplets are forced to excite by the boundary condition. We find that the droplets have nontrivial fractal dimension not only for its surface but also for its volume, in contrast to what has been implicitly assumed in conventional droplet arguments.

Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.

The origin of entanglement in a class of three-dimensional spin models, at low momenta, is traced to topological reasons. The establishment of the result is facilitated by the gauge principle which, in conjunction with the duality mapping of the spin models, enables us to recast them as lattice Chern–Simons theories. The entanglement measures are expressed in terms of the correlators of Wilson lines, loops, and their generalisations. For continuous spins, these yield the invariants of knots and links. For Ising-like models, they can be expressed in terms of three-manifold invariants obtained from finite group cohomology — the so-called Dijkgraaf–Witten invariants.

Dirty quantum Hall ferromagnets (QHFMs) provide a setting both for new problems in the theory of magnetism with quenched disorder, and for new realisations of old problems. In the first category, the fact that spin textures in Heisenberg QHFMs carry charge leads to a coupling between charged impurities and magnetic order. This coupling drives a zero-temperature transition between a ferromagnet at low disorder and a spin glass at strong disorder, and controls screening and the nature of excitations in the disorder-dominated ground state. In the second category, random fields coupling linearly to the order parameter appear in some Ising QHFMs, and transport measurements appear to indicate field-induced domain states at low temperature.

After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a unified way many numerical results for two-, three- and four-dimensional models including the ±J Ising model, random Potts model, random lattice gauge theory, and random Z_q model. It is also suggested from the same theoretical framework that models with symmetric distribution of randomness in exchange interaction have no finite-temperature transition on the square lattice.

A brief introduction and overview is given of the complexity that is possible and the challenges its study poses in many-body systems in which spatial dimension is irrelevant and naively one might have expected trivial behaviour.

Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this work we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value α_cm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At α_cm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.

The paper reviews the entanglement behavior of a 2-qubit system in a quantum spin glass using the Heisenberg XX model and the interaction of the system with a spin glass bath environment. In the first part, we study the entanglement (concurrence) for a 3- and 4-qubit with nearest neighbor interaction. With a fixed mean and varying standard deviation for the J coupling, the concurrence is numerically plotted with temperature for the different configurations. A general formula for the concurrence is given for n qubits at low temperature. In the second part, we study the concurrence of a 2-qubit system coupled to a spin glass bath environment with n = 2 to ≥ 4 qubits. The bath sites are coupled with random J coupling and varying applied magnetic field. A general formula for concurrence is given for mean J = 0 and B = 0 for n bath sites. For small random J and magnetic field B, a steady state is obtained with an approximate concurrence of 0.5, showing that the entanglement is preserved.

We investigate the Kondo resistivity using the perturbation methods. We calculate the resistivity above the Kondo temperature using an adjustable infinite series or series from log-function for uncrossed Kondo diagrams. We obtain the energy eigenvalue above the spin glass temperature using this RISM.