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Search Results: 1 - 10 of 466957 matches for " A. Alan Middleton "
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Thermal Rounding of the Charge Density Wave Depinning Transition
A. Alan Middleton
Physics , 1992, DOI: 10.1103/PhysRevB.45.9465
Abstract: The rounding of the charge density wave depinning transition by thermal noise is examined. Hops by localized modes over small barriers trigger ``avalanches'', resulting in a creep velocity much larger than that expected from comparing thermal energies with typical barriers. For a field equal to the $T=0$ depinning field, the creep velocity is predicted to have a {\em power-law} dependence on the temperature $T$; numerical computations confirm this result. The predicted order of magnitude of the thermal rounding of the depinning transition is consistent with rounding seen in experiment.
Disorder-Induced Topological Defects in a d=2 Elastic Medium at Zero Temperature
A. Alan Middleton
Physics , 1998, DOI: 10.1103/PhysRevB.61.14787
Abstract: The density and correlations of topological defects are investigated numerically in a model of a d=2 elastic medium subject to a periodic quenched random potential. The computed density of defects decreases approximately exponentially with the defect core energy. Comparing the defect-free ground state with the ground state with defects, it is found that the difference is described by string-like excitations, bounded by defect pairs, which have a fractal dimension of 1.250(3). At zero temperature, the disorder-induced defects screen the interaction of introduced vortex pairs.
Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder
A. Alan Middleton
Physics , 1999, DOI: 10.1103/PhysRevLett.83.1672
Abstract: The effect of open boundary conditions for four models with quenched disorder are studied in finite samples by numerical ground state calculations. Extrapolation to the infinite volume limit indicates that the configurations in ``windows'' of fixed size converge to a unique configuration, up to global symmetries. The scaling of this convergence is consistent with calculations based on the fractal dimension of domain walls. These results provide strong evidence for the ``two-state'' picture of the low temperature behavior of these models. Convergence in three-dimensional systems can require relatively large windows.
Numerical Results for the Ground-State Interface in a Random Medium
A. Alan Middleton
Physics , 1995, DOI: 10.1103/PhysRevE.52.R3337
Abstract: The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These results are compared with previous analytical and numerical estimates.
Scaling, domains, and states in the four-dimensional random field Ising magnet
A. Alan Middleton
Physics , 2002,
Abstract: The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As the magnetization exponent $\beta$ is more easily distinguishable from zero in four dimensions than in three dimensions, these results provide a useful test of conventional scaling theories. Results are presented for the critical behavior of the heat capacity, magnetization, and stiffness. The fractal dimensions of the domain walls at criticality are estimated. A notable difference from three dimensions is the structure of the spin domains: frozen spins of both signs percolate at a disorder magnitude less than the value at the ferromagnetic to paramagnetic transition. Hence, in the vicinity of the transition, there are two percolating clusters of opposite spins that are fixed under any boundary conditions. This structure changes the interpretation of the domain walls for the four dimensional case. The scaling of the effect of boundary conditions on the interior spin configuration is found to be consistent with the domain wall dimension. There is no evidence of a glassy phase: there appears to be a single transition from two ferromagnetic states to a single paramagnetic state, as in three dimensions. The slowing down of the ground state algorithm is also used to study this model and the links between combinatorial optimization and critical behavior.
Improved extremal optimization for the Ising spin glass
A. Alan Middleton
Physics , 2004, DOI: 10.1103/PhysRevE.69.055701
Abstract: A version of the extremal optimization (EO) algorithm introduced by Boettcher and Percus is tested on 2D and 3D spin glasses with Gaussian disorder. EO preferentially flips spins that are locally ``unfit''; the variant introduced here reduces the probability to flip previously selected spins. Relative to EO, this adaptive algorithm finds exact ground states with a speed-up of order $10^{4}$ ($10^{2}$) for $16^{2}$- ($8^{3}$-) spin samples. This speed-up increases rapidly with system size, making this heuristic a useful tool in the study of materials with quenched disorder.
Computational Complexity of Determining the Barriers to Interface Motion in Random Systems
A. Alan Middleton
Physics , 1999, DOI: 10.1103/PhysRevE.59.2571
Abstract: The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative features of the energy landscape of such a many-degree-of-freedom system are the ground-state energy and the magnitude of the energy barriers between given configurations. While the numerical determination of the former can be accomplished in time polynomial in the system size, it is shown here that the problem of determining the latter quantity is NP-complete. Exact computation of barriers is therefore (almost certainly) much more difficult than determining the exact ground states of interfaces.
Energetics and geometry of excitations in random systems
A. Alan Middleton
Physics , 2000, DOI: 10.1103/PhysRevB.63.060202
Abstract: Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.
Which measures of spin-glass overlaps are informative?
A. Alan Middleton
Physics , 2013, DOI: 10.1103/PhysRevB.87.220201
Abstract: The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional spin glasses indicate that common measures of P(q) in smaller samples do not decide between theoretical pictures. Strong corrections result from P(q) being an average over many scales, as seen in a toy droplet model. However, the median of the integrals of sample-dependent P(q) curves shows promise for deciding the thermodynamic behavior.
Critical slowing down in polynomial time algorithms
A. Alan Middleton
Physics , 2001, DOI: 10.1103/PhysRevLett.88.017202
Abstract: Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of the model, including vanishing stiffness on scales beyond the correlation length and the ground state degeneracy, the number of operations carried out by one such algorithm, the push-relabel algorithm for the random field Ising model, can be estimated. Some scaling can also be predicted for the 2D spin glass.
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