Search results for "Neural"
showing 10 items of 2783 documents
Ising Spin-Glass on a Lattice with Small Loops
1991
We consider the Ising spin-glass on a special lattice containing small loops with finite coordination number c. We derive the equation for the effective field distribution. With zero external field, we calculate the spin-glass transition temperature and obtain the lower critical dimension of the system. We investigate the system near and below the spin-glass transition and find that the replica symmetric solution is unstable in the low-temperature phase. Our results indicate that the replica symmetry breaking (RSB) effects are stronger than that of the Bethe lattice and furthermore, RSB is enhanced as the dimension (c/2) is decreased. Comparison with recent results of the 1/d expansion is a…
Multioverlap Simulations of the 3D Edwards-Anderson Ising Spin Glass
1997
We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by re-weighting. We demonstrate the feasibility of the approach by studying the $3d$ Edwards-Anderson Ising ($J_{ik}=\pm 1$) spin glass in the broken phase ($\beta=1$). For the first time it becomes possible to obtain reliable results about spin glass tunneling barriers. In addition, as do some earlier numerical studies, our results support that Parisi mean field theory is valid down to $3d$.
Griffiths phase manifestation in disordered dielectrics
2000
We predict the existence of Griffith phase in the dielectrics with concentrational crossover between dipole glass (electric analog of spin glass) and ferroelectricity. The peculiar representatives of above substances are $KTaO_3:Li$, $Nb$, $Na$ or relaxor ferroelectrics like $Pb_{1-x}La_xZr_{0.65}Ti_{0.35}O_3$. Since this phase exists above ferroelectric phase transition temperature (but below that temperature for ordered substance), we call it "para-glass phase". We assert that the difference between paraelectric and para-glass phase of above substances is the existence of clusters (inherent to "ordinary" Griffiths phase in Ising magnets) of correlated dipoles. We show that randomness play…
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.
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 …
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 …
Transient Reversible Growth and Percolation During Phase Separation
1988
Binary mixtures when quenched into the two-phase region exhibit transient percolation phenomena. These transient percolation phenomena and the underlying mechanism of transient reversible growth are investigated. In particular, one of the possible dynamical percolation lines between the dynamical spinodal and the line of macroscopic percolation is traced out. Analyzing the finite size effects with the usual scaling theory one finds exponents which seem to be inconsistent with the universality class of percolation. However, at zero temperature, where the growth is non-reversible and the transition of a sol-gel type, the exponents are consistent with those of random percolation.
How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?
1998
Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.