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Full-Text Articles in Physics

Low-Temperature Behavior Of The Statistics Of The Overlap Distribution In Ising Spin-Glass Models, Matthew Wittmann, B. Yucesoy, Helmut G. Katzgraber, Jonathan Machta, A. P. Young Dec 2013

Low-Temperature Behavior Of The Statistics Of The Overlap Distribution In Ising Spin-Glass Models, Matthew Wittmann, B. Yucesoy, Helmut G. Katzgraber, Jonathan Machta, A. P. Young

Jonathan Machta

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and four space dimensions, and one-dimensional long-range models with diluted power-law interactions. We study three long-range models with different powers as follows: The first is approximately equivalent to a short-range model in three dimensions, the second to a short-range model in four dimensions, and the third to a short-range model in the mean-field regime. We study an observable proposed earlier by some of us which aims to distinguish the “replica symmetry breaking ...


Erratum: Glassy Chimeras Could Be Blind To Quantum Speedup: Designing Better Benchmarks For Quantum Annealing Machines, Martin Weigel, Helmut G. Katzgraber, Jonathan Machta, Firas Hamze, Ruben S. Andrist Dec 2013

Erratum: Glassy Chimeras Could Be Blind To Quantum Speedup: Designing Better Benchmarks For Quantum Annealing Machines, Martin Weigel, Helmut G. Katzgraber, Jonathan Machta, Firas Hamze, Ruben S. Andrist

Jonathan Machta

No abstract provided.


Evidence Against A Mean-Field Description Of Short-Range Spin Glasses Revealed Through Thermal Boundary Conditions, Wenlong Wang, Jonathan Machta, Helmut G. Katzgraber Dec 2013

Evidence Against A Mean-Field Description Of Short-Range Spin Glasses Revealed Through Thermal Boundary Conditions, Wenlong Wang, Jonathan Machta, Helmut G. Katzgraber

Jonathan Machta

A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states, or theories that are based on infinitely many pure states—such as replica symmetry breaking—best describe realistic short-range systems. To resolve this controversy, the three-dimensional Edwards-Anderson Ising spin glass in thermal boundary conditions is studied numerically using population annealing Monte Carlo. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights ...


Correlations Between The Dynamics Of Parallel Tempering And The Free Energy Landscape In Spin Glasses, Burcu Yucesoy, Jonathan Machta, Helmut G. Katzgraber Dec 2012

Correlations Between The Dynamics Of Parallel Tempering And The Free Energy Landscape In Spin Glasses, Burcu Yucesoy, Jonathan Machta, Helmut G. Katzgraber

Jonathan Machta

We present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using parallel tempering (replica exchange) Monte Carlo we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape.


Nature Vs. Nurture: Predictability In Low-Temperature Ising Dynamics, J. Ye, Jonathan Machta, C. M. Newman, D. L. Stein Dec 2012

Nature Vs. Nurture: Predictability In Low-Temperature Ising Dynamics, J. Ye, Jonathan Machta, C. M. Newman, D. L. Stein

Jonathan Machta

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state (“nature”) versus the realization of the stochastic dynamics (“nurture”) in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from T=∞ to T=0. We performed Monte Carlo studies on the overlap between “identical twins” raised in independent dynamical environments, up to size L=500. Our results suggest an overlap decaying with time as t−θh with θh=0.22±0.02; the same exponent holds for ...


Evidence Of Non-Mean-Field-Like Low-Temperature Behavior In The Edwards-Anderson Spin-Glass Model, B. Yucesoy, Helmut G. Katzgraber, Jonathan Machta Oct 2012

Evidence Of Non-Mean-Field-Like Low-Temperature Behavior In The Edwards-Anderson Spin-Glass Model, B. Yucesoy, Helmut G. Katzgraber, Jonathan Machta

Jonathan Machta

The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.


Computational Study Of A Multistep Height Model, Matthew Drake, Jonathan Machta, Youjin Deng, Douglas Abraham, Charles Newman Mar 2012

Computational Study Of A Multistep Height Model, Matthew Drake, Jonathan Machta, Youjin Deng, Douglas Abraham, Charles Newman

Jonathan Machta

An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL, 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the model reduces to the two-dimensional Ising model in the height representation. When the Ising model constraint of single height steps is relaxed, the critical temperature and critical exponents are continuously varying functions of the parameter controlling height steps larger than one. Numerical estimates of the critical exponents can be mapped via a single parameter-- the Coulomb gas coupling-- to the exponents of the O(n) loop model on the honeycomb lattice ...


Critical Behavior Of The Chayes–Machta–Swendsen–Wang Dynamics, Y Deng, T Garoni, J Machta, G Ossola, M Polin, A Sokal Mar 2011

Critical Behavior Of The Chayes–Machta–Swendsen–Wang Dynamics, Y Deng, T Garoni, J Machta, G Ossola, M Polin, A Sokal

Jonathan Machta

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z≥α/ν is close to but probably not sharp in d=2 and is far from sharp in d=3, for all q. The conjecture z≥β/ν is false (for some values of q) in both d=2 and d=3.


Internal Diffusion-Limited Aggregation: Parallel Algorithms And Complexity, C Moore, J Machta Mar 2011

Internal Diffusion-Limited Aggregation: Parallel Algorithms And Complexity, C Moore, J Machta

Jonathan Machta

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set of paths is complete for the complexity class CC, the subset of P characterized by circuits composed of comparator gates. CC-completeness is believed to imply that, in the worst case, growing a cluster of size n requires polynomial time in n even on a parallel computer. A parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to ...


Parallel Complexity Of Random Boolean Circuits, Jonathan Machta, S. Dedeo, S. Mertens, C. Moore Dec 2010

Parallel Complexity Of Random Boolean Circuits, Jonathan Machta, S. Dedeo, S. Mertens, C. Moore

Jonathan Machta

Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a massively parallel computer, in a time much less than the depth of the circuit. Nonetheless, it is found that, for some ensembles of random circuits, saturation to a fixed truth value occurs rapidly so that evaluation of the circuit can be accomplished in much less parallel time than the depth of the circuit. For other ensembles saturation does not occur and circuit evaluation ...


Monte Carlo Methods For Rough Free Energy Landscapes: Population Annealing And Parallel Tempering, Jonathan Machta, Richard S. Ellis Dec 2010

Monte Carlo Methods For Rough Free Energy Landscapes: Population Annealing And Parallel Tempering, Jonathan Machta, Richard S. Ellis

Jonathan Machta

Parallel tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiencies of the two methods are compared. For large systems, population annealing is closer to equilibrium than parallel tempering for short simulations. However, with respect to the amount of computation, parallel tempering converges exponentially while population annealing converges only inversely. As ...


Population Annealing With Weighted Averages: A Monte Carlo Method For Rough Free-Energy Landscapes, Jonathan Machta Dec 2009

Population Annealing With Weighted Averages: A Monte Carlo Method For Rough Free-Energy Landscapes, Jonathan Machta

Jonathan Machta

The population annealing algorithm introduced by Hukushima and Iba is described. Population annealing combines simulated annealing and Boltzmann weighted differential reproduction within a population of replicas to sample equilibrium states. Population annealing gives direct access to the free energy. It is shown that unbiased measurements of observables can be obtained by weighted averages over many runs with weight factors related to the free-energy estimate from the run. Population annealing is well suited to parallelization and may be a useful alternative to parallel tempering for systems with rough free-energy landscapes such as spin glasses. The method is demonstrated for spin glasses.


A Percolation-Theoretic Approach To Spin Glass Phase Transitions, Jonathan Machta, C. M. Newman, D. L. Stein Dec 2008

A Percolation-Theoretic Approach To Spin Glass Phase Transitions, Jonathan Machta, C. M. Newman, D. L. Stein

Jonathan Machta

The magnetically ordered, low temperature phase of Ising ferromagnets is manifested within the associated Fortuin—Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering — both in the short-range Edwards—Anderson (EA) and infinite-range Sherrington—Kirkpatrick (SK) models — within a tworeplica FK representation and also in the different Chayes—Machta—Redner two-replica graphical representation. Numerical studies of the ±J EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that ...


The Percolation Signature Of The Spin Glass Transition, Jonathan Machta, C. M. Newman, D. L. Stein Dec 2007

The Percolation Signature Of The Spin Glass Transition, Jonathan Machta, C. M. Newman, D. L. Stein

Jonathan Machta

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin–Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering—both in short-range (EA) and infinite-range (SK) models—within a two-replica FK representation and also within the different Chayes–Machta–Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating ...


Percolation In The Sherrington-Kirkpatrick Spin Glass, Jonathan Machta, C. M. Newman, D. L. Stein Dec 2007

Percolation In The Sherrington-Kirkpatrick Spin Glass, Jonathan Machta, C. M. Newman, D. L. Stein

Jonathan Machta

We present extended versions and give detailed proofs of results about percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The ...


Complexity, Parallel Computation And Statistical Physics, Jonathan Machta Dec 2005

Complexity, Parallel Computation And Statistical Physics, Jonathan Machta

Jonathan Machta

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history that is applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics


Ground States And Thermal States Of The Random Field Ising Model, Yong Wu, Jonathan Machta Dec 2004

Ground States And Thermal States Of The Random Field Ising Model, Yong Wu, Jonathan Machta

Jonathan Machta

The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random field and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated—a concrete manifestation of the zero temperature fixed point ...


Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, Jonathan Machta Dec 2004

Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, Jonathan Machta

Jonathan Machta

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v)∼v−σ. The exponent σ is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting ...


Structural And Computational Depth Of Diffusion Limited Aggregation, D. Tillberg, Jonathan Machta Dec 2003

Structural And Computational Depth Of Diffusion Limited Aggregation, D. Tillberg, Jonathan Machta

Jonathan Machta

Diffusion-limited aggregation (DLA) is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the depth of the tree defined by the cluster. The existence of this algorithm suggests a connection between a fundamental computational and structural property of DLA.


Ground State Numerical Study Of The Three-Dimensional Random Field Ising Model, I. Dukovski, Jonathan Machta Dec 2002

Ground State Numerical Study Of The Three-Dimensional Random Field Ising Model, I. Dukovski, Jonathan Machta

Jonathan Machta

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 603. For each realization of the normalized random fields, the strength of the random field, Δ and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H−Δ plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents ...


Invaded Cluster Simulations Of The Xy Model In Two And Three, I. Dukovski, Jonathan Machta, L. V. Chayes Dec 2001

Invaded Cluster Simulations Of The Xy Model In Two And Three, I. Dukovski, Jonathan Machta, L. V. Chayes

Jonathan Machta

The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 20002 and 1203, respectively. A soft spin O(2) model, in the same universality class as the three-dimensional XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are Kc=0.45412(2) for the three-dimensional XY model and η=0.037(2) for the three-dimensional XY universality class. For the two-dimensional XY model the results are Kc=1.120(1) and η=0.251(5). The invaded ...


Parallel Dynamics And Computational Complexity Of The Bak-Sneppen Model, Jonathan Machta, X. N. Li Dec 2000

Parallel Dynamics And Computational Complexity Of The Bak-Sneppen Model, Jonathan Machta, X. N. Li

Jonathan Machta

No abstract provided.


Critical Dynamics Of Two-Replica Cluster Algorithms, X. N. Li, Jonathan Machta Dec 2000

Critical Dynamics Of Two-Replica Cluster Algorithms, X. N. Li, Jonathan Machta

Jonathan Machta

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0129183101001663


Cluster Monte Carlo Study Of Multicomponent Fluids Of The Stillinger-Helfand And Widom-Rowlinson Type, Rongfeng Sun, Harvey Gould, Jonathan Machta, L. W. Chayes Dec 1999

Cluster Monte Carlo Study Of Multicomponent Fluids Of The Stillinger-Helfand And Widom-Rowlinson Type, Rongfeng Sun, Harvey Gould, Jonathan Machta, L. W. Chayes

Jonathan Machta

Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not interact, but particles of different types interact with each other via a repulsive potential. Examples of interactions include the Gaussian molecule potential and a repulsive step potential. Accurate values of the critical density, fugacity, and magnetic exponent are found in two and three dimensions for the two-species model. The effect of varying the number of species and of introducing quenched impurities is also investigated. In all the cases studied ...