arXiv subjects

A. P. Young

Publications and source records attributed to A. P. Young.

At least 73 records · Page 4Linked to original sources

arXiv2003

Ensemble dependence in the Random transverse-field Ising chain

In a disordered system one can either consider a microcanonical ensemble, where there is a precise constraint on the random variables, or a canonical ensemble where the variables are chosen according to a distribution without constraints. We address the question as to whether critical exponents in these two cases can differ through a detailed study of the random transverse-field Ising chain. We find that the exponents are the same in both ensembles, though some critical amplitudes vanish in the microcanonical ensemble for correlations which span the whole system and are particularly sensitive to the constraint. This can \textit{appear} as a different exponent. We expect that this apparent dependence of exponents on ensemble is related to the integrability of the model, and would not occur in non-integrable models.

cond-mat.dis-nn↗

arXiv2003

Low Energy Excitations in Spin Glasses from Exact Ground States

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent θ', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.

cond-mat.dis-nn↗

arXiv2003

Energetics of clusters in the two-dimensional Ising spin glass

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relatively good agreement with standard domain wall calculations.

cond-mat.dis-nn↗

arXiv2003

Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

We present results from Monte Carlo simulations of the one-dimensional Ising spin glass with power-law interactions at low temperature, using the parallel tempering Monte Carlo method. For a set of parameters where the long-range part of the interaction is relevant, we find evidence for large-scale droplet-like excitations with an energy that is independent of system size, consistent with replica symmetry breaking. We also perform zero-temperature defect energy calculations for a range of parameters and find a stiffness exponent for domain walls in reasonable, but by no means perfect agreement with analytic predictions.

cond-mat.dis-nn↗

arXiv2003

Interface energies in Ising spin glasses

The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes but after allowing for fluctuation effects, a non-zero interface free energy is obtained which is significantly different from numerical expectations.

cond-mat.dis-nn↗

arXiv2002

Numerical studies of the two- and three-dimensional gauge glass at low temperature

We present results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using the parallel tempering Monte Carlo method. Our results in two dimensions strongly support the transition being at T_c=0. A finite-size scaling analysis, which works well only for the larger sizes and lower temperatures, gives the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01, compatible with recent results from domain wall renormalization group studies.

cond-mat.dis-nn↗

arXiv2002

Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass

We study large-scale, low-energy excitations in the Ising spin glass with Gaussian interactions in two-dimensions at zero temperature, using an optimization algorithm to determine exact ground states. Periodic boundary conditions are applied. Our results for the fractal dimension of the surface, d_s, and stiffness exponent, theta', for "droplet" excitations, are in reasonable agreement with estimates from "domain wall" calculations, and so support the predictions of the "droplet theory". Restricting our analysis to small lattices, we do not find an effective value of theta' close to -0.47 as has been recently proposed. The effects of averaging over droplets of different sizes are studied and are also found to be too small to give theta' approx -0.47 for smaller sizes. Larger corrections to finite-size scaling would be needed in three and four dimensions in order for the numerical data used to support the "TNT" scenario to be compatible with the droplet theory prediction that the stiffness exponent is the same for droplets and domain walls.

cond-mat.dis-nn↗

arXiv2002

The stiffness exponent of two-dimensional Ising spin glasses for non-periodic boundary conditions using aspect-ratio scaling

We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at T=0 in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size LxM with different aspect-ratios 1/8 <= L/M <= 64 are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent theta=-0.287(4), which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.

cond-mat.dis-nn↗

arXiv2002

Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions

We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.

cond-mat.dis-nn↗

arXiv2002

Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures

We report results for simulations of the four-dimensional XY spin glass using the parallel tempering Monte Carlo method at low temperatures for moderate sizes. Our results are qualitatively consistent with earlier work on the three-dimensional gauge glass as well as three- and four-dimensional Edwards-Anderson Ising spin glass. An extrapolation of our results would indicate that large-scale excitations cost only a finite amount of energy in the thermodynamic limit. The surface of these excitations may be fractal, although we cannot rule out a scenario compatible with replica symmetry breaking in which the surface of low-energy large-scale excitations is space filling.

cond-mat.dis-nn↗

arXiv2002

Monte Carlo simulations of spin glasses at low temperatures: Effects of free boundary conditions

We present results of Monte Carlo simulations, using parallel tempering, on the three- and four-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings at low temperatures with free boundary conditions. Our results suggest that large-scale low-energy excitations may be space filling. The data implies that the energy of these excitations increases with increasing system size for small systems, but we see evidence in three dimensions, where we have a greater range of sizes, for a crossover to a regime where the energy is independent of system size, in accordance with replica symmetry breaking.

cond-mat.dis-nn↗

arXiv2001

Nature of the Spin-glass State in the Three-dimensional Gauge Glass

We present results from simulations of the gauge glass model in three dimensions using the parallel tempering Monte Carlo technique. Critical fluctuations should not affect the data since we equilibrate down to low temperatures, for moderate sizes. Our results are qualitatively consistent with earlier work on the three and four dimensional Edwards-Anderson Ising spin glass. We find that large scale excitations cost only a finite amount of energy in the thermodynamic limit, and that those excitations have a surface whose fractal dimension is less than the space dimension, consistent with a scenario proposed by Krzakala and Martin, and Palassini and Young.

cond-mat.dis-nn↗

arXiv2001

Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations

Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different strengths h of the random fields and sizes up to N=96^3 are considered. By numerically differentiating the bond-energy with respect to h a specific-heat like quantity is obtained, which does not appear to diverge at the critical point but rather exhibits a cusp. We also consider the effect of a small uniform magnetic field, which allows us to calculate the T=0 susceptibility. From a finite-size scaling analysis, we obtain the critical exponents ν=1.32(7), α=-0.63(7), η=0.50(3) and find that the critical strength of the random field is h_c=2.28(1). We discuss the significance of the result that αappears to be strongly negative.

cond-mat.dis-nn↗

arXiv2001

Convergence of Monte Carlo Simulations to Equilibrium

We give two direct, elementary proofs that a Monte Carlo simulation converges to equilibrium provided that appropriate conditions are satisfied. The first proof requires detailed balance while the second is quite general.

cond-mat.stat-mech↗

arXiv2001

State Hierarchy Induced by Correlated Spin Domains in short range spin glasses

We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed method using clustering. The analysis reveals a hierarchical state space structure. At each level of the hierarchy states are labeled by the orientations of a set of correlated macroscopic spin domains. Our picture of the low temperature phase of short range spin glasses is that of a State Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low temperature phase is manifest in the fact that the composition of such a spin domain (i.e. its constituent spins), as well as its identifying label, are defined and determined by the ``location'' in the state hierarchy at which it appears. Mapping out the phase space structure by means of the orientations assumed by these domains enhances our ability to investigate the overlap distribution, which we find to be non-trivial. Evidence is also presented that these states may have a non-ultrametric structure.

cond-mat.dis-nn↗

arXiv2001

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^θ, with θ=-0.266(2) and θ=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so θ= 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.

cond-mat.dis-nn↗

arXiv2001

Monte Carlo Simulations of Spin Glasses at Low Temperatures

We report the results of Monte Carlo simulations on several spin glass models at low temperatures. By using the parallel tempering (Exchange Monte Carlo) technique we are able to equilibrate down to low temperatures, for moderate sizes, and hence the data should not be affected by critical fluctuations. Our results for short range models are consistent with a picture proposed earlier that there are large scale excitations which cost only a finite energy in the thermodynamic limit, and these excitations have a surface whose fractal dimension is less than the space dimension. For the infinite range Viana-Bray model, our results obtained for a similar number of spins are consistent with standard replica symmetry breaking.

cond-mat.dis-nn↗

arXiv2001

The +/-J Spin Glass: Effects of Ground State Degeneracy

We perform Monte Carlo simulations of the Ising spin glass at low temperature in three dimensions with a +/-J distribution of couplings. Our results display crossover scaling between T=0 behavior, where the order parameter distribution P(q) becomes trivial for L -> $\infty$, and finite-T behavior, where the non-trivial part of P(q) has a much weaker dependence on the size L, and is possibly size independent.

cond-mat.dis-nn↗