Search results for " Glass"
showing 10 items of 409 documents
Monte Carlo study of the bimodal three-state Potts glass
1992
Employing Monte Carlo simulations, we compute the spin-glass susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) of the three-state Potts glass model on a simple-cubic lattice for various temperatures and lattice sizes ranging from L=4 to 10. We use the discrete \ifmmode\pm\else\textpm\fi{}J distribution for the bonds. Comparing our results with a recent high-temperature series expansion, we find a systematic deviation at lower temperatures, which cannot be explained by finite-size effects in our data. The low-temperature behavior of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) is compatible with d = 3 being the lower critical dimension of this model.
Multi-overlap simulations of free-energy barriers in the 3D Edwards–Anderson Ising spin glass
1999
We report large-scale simulations of the three-dimensional Edwards‐Anderson Ising spin-glass model using the multi-overlap Monte Carlo algorithm. We present our results in the spin-glass phase on free-energy barriers and the non-trivial finite-size scaling behavior of the Parisi order-parameter distribution. © 1999 Elsevier Science B.V. All rights reserved.
Kinetics of Ordered Phases in Finite Spin Systems
1989
We study the growth of the ordered phase in a spin system of finite size suddenly brought below the transition temperature. Such a growth is driven by the instability of the mode corresponding to the largest eigenvalue of the interaction matrix. The relaxation occurs through different regimes according to whether the unstable mode has a negligible or macroscopic amplitude. One regime is characterised by dynamical scaling properties whereas in the other we can distinguish the growth to a macroscopic amplitude followed by rare transitions from one equilibrium amplitude to another. The analysis is carried out in the framework of a dynamical generalisation of the spherical model assuming non-ra…
Monte Carlo study of the order-parameter distribution in the four-dimensional Ising spin glass
1990
We investigate the order-parameter distribution P(q) of the Ising spin glass with nearest-neighbor interactions in four dimensions using Monte Carlo simulations on lattices of linear dimension up to L=6. We find that, below the transition temperature ${\mathit{T}}_{\mathit{c}}$, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.
Spin glasses: Experimental facts, theoretical concepts, and open questions
1986
This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed …
Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation
2002
We use Monte Carlo simulations, single spin-flip as well as parallel tempering techniques to investigate the 10-state fully connected Potts glass for system sizes of up to N = 2560. We find that the α-relaxation shows a strong dependence on N and that for the system sizes considered the system remains ergodic even at temperatures below T D , the dynamical critical temperature for this model. However, if one uses the data for the finite size systems, such as the relaxation times or the time dependence of the spin autocorrelation function, and extrapolates them to the thermodynamic limit, one finds that they are indeed compatible with the results for N = ∞ (which are known from analytical cal…
A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
2001
A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100^2 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential and not as a power law as T -> Tc = 0.
High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices
1999
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings \(\). In these star-graph expansions up to order 22 in the inverse temperature \(\), the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling Kc and the critical exponent \(\) of the spin-glass susceptibility in a large region of …
Dynamics of Ising spin glasses far below the lower critical dimension: The one-dimensional case and small clusters
1985
The Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field. For small clusters of spins (closed rings ofN bonds, withN≦7) the complex magnetic susceptibility χ(ω) and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {Jij} by diagonalization of the Liouville operator; apart from the ±J model, the average over {Jij} must be done numerically by simple random sampling Monte Carlo. Nevertheless our accuracy is much better than corresponding dynamic Monte Carlo simulations, even if one considers the extrapolation toN→∞.
Vortex-glass transition in three dimensions.
1991
We investigate the possibility of a vortex-glass transition in a disordered type-II superconductor in a magnetic field in three dimensions by numerical studies of a simplified model. Monte Carlo simulations at finite temperature and domain-wall renormalization-group calculations at {ital T}=0 indicate that {ital d}=3 is just above the lower critical dimension {ital d}{sub {ital l}}, though the possibility that {ital d}{sub {ital l}}=3 cannot be definitely ruled out. A comparison is made with {ital XY} and Ising spin glasses. The (effective) correlation-length exponent {nu} and dynamical exponent {ital z} are in fairly good agreement with experiment.