Search results for "spin glass"
showing 10 items of 64 documents
Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium
1999
By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We study both one time quantities and two-times correlation functions. Two-times correlation functions show a strong time and waiting time $t_w$ dependence. For large $t_w$ and times corresponding to the early $\beta$-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. at long times $\tau$ the correlation functions can be expressed as $C_{\rm AG}(h(t_w+\tau)/h(t_w))$ and compute the function $h(t)$. This function is found to show a $t$-depen…
High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass
2019
In two dimensions, short-range spin glasses order only at zero temperature, where efficient combinatorial optimization techniques can be used to study these systems with high precision. The use of large system sizes and high statistics in disorder averages allows for reliable finite-size extrapolations to the thermodynamic limit. Here, we use a recently introduced mapping of the Ising spin-glass ground-state problem to a minimum-weight perfect matching problem on a sparse auxiliary graph to study square-lattice samples of up to 10 000 × 10 000 spins. We propose a windowing technique that allows to extend this method, that is formally restricted to planar graphs, to the case of systems with …
Theory of orientational glasses models, concepts, simulations
1992
Abstract This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former…
The four dimensional Ising spin glass: A Monte Carlo study (invited)
1991
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.
MC Study of the p-state Mean-Field Potts Glass
1999
The p-state mean-field Potts glass with ±J-couplings is studied by Monte Carlo (MC) simulations, both for p = 3 and p = 6 states. At the exactly known glass transition temperature Tc, the moments q( k ) of the spin glass order parameter satisfy for p = 3 a simple scaling behavior, q( k ) \({q^{\left( k \right)}}\alpha {N^{ - k/3}}{\tilde f_k}\left\{ {{N^{1/3}}\left( {1 - T/{T_c}} \right)} \right\},k = 1,2,3,...\). The specific-heat maxima exhibit a similar behavior, c V max α const — N -l/3, while the approach of the maxima positions T max to T c as N → ∞ is non-monotonic. For p = 6 the results are compatible with the expected result of a quite peculiar first-order phase transition. The spe…
Two-dimensional isotropic orientational glasses: a computer-simulation study
1989
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction. It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to “ferromagnetic” correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT→0, and the critical exponents for this zero-temperature phase transition are estimated. Dynamic correlation functions are analyzed as well and it is s…
Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass
1991
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…
Domain-wall excitations in the two-dimensional Ising spin glass
2018
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to $10\,000\times 10\,000$ spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic…
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 $3d$.