0000000000332056
AUTHOR
A. P. Young
Monte Carlo study of the order-parameter distribution in the four-dimensional Ising spin glass
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.
Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass
During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. T…
Finite-size tests of hyperscaling.
The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.
Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.
For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.
Spin glasses: Experimental facts, theoretical concepts, and open questions
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 …
Vortex-glass transition in three dimensions.
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.
The Ground State of the 2-Dimensional Potts Glass
We study the ground state of the 3-state Potts glass in 2 dimensions with a Gaussian distribution of couplings by domain wall renormalization group techniques. We find that the glass correlation function decays to a finite value within a distance of about 2.4 lattice spacings. Thus, there is long-range order in the ground state even though, as found earlier, there is a finite zero-point entropy.
The four dimensional Ising spin glass: A Monte Carlo study (invited)
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.