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A. P. Young

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

At least 37 records · Page 2Linked to original sources
arXiv2012

Solving the Graph Isomorphism Problem with a Quantum Annealer

We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are isomorphic (i.e., can be transformed into each other simply by a relabeling of the vertices). We demonstrate the capabilities of the method by analyzing several types of graph families, focusing on graphs with particularly high symmetry called strongly regular graphs (SRG's). We also show that our method is applicable, within certain limitations, to currently available quantum hardware such as "D-Wave One".

quant-ph↗
arXiv2012

The correspondence between long-range and short-range spin glasses

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.

cond-mat.dis-nn↗
arXiv2012

Spin glasses in the non-extensive regime

Spin systems with long-range interactions are "non-extensive" if the strength of the interactions falls off sufficiently slowly with distance. It has been conjectured for ferromagnets, and more recently for spin glasses, that, everywhere in the non-extensive regime, the free energy is exactly equal to that for the infinite range model in which the characteristic strength of the interaction is independent of distance. In this paper we present the results of Monte Carlo simulations of the one-dimensional long-range spin glasses in the non-extensive regime. Using finite-size scaling, our results for the transition temperatures are consistent with this prediction. We also propose, and provide numerical evidence for, an analogous result for diluted long-range spin glasses in which the coordination number is finite, namely that the transition temperature throughout the non-extensive regime is equal to that of the infinite-range model known as the Viana-Bray model.

cond-mat.dis-nn↗
arXiv2011

Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical" instances. We find that at large sizes N, the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm the harder it is also for the quantum adiabatic algorithm.

cond-mat.stat-mech↗
arXiv2011

Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses

We test for the presence or absence of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg spin glass model, in which the rms strength of the interactions decays with distance, r as 1/r^{sigma}. It is argued that varying the power sigma is analogous to varying the space dimension d in a short-range model. For sigma=0.6, which is in the mean field regime regime, we find clear evidence for an AT line. For sigma = 0.85, which is in the non-mean-field regime and corresponds to a space dimension of close to 3, we find no AT line, though we cannot rule one out for very small fields. Finally for sigma=0.75, which is in the non-mean-field regime but closer to the mean-field boundary, the evidence suggests that there is an AT line, though the possibility that even larger sizes are needed to see the asymptotic behavior can not be ruled out.

cond-mat.dis-nn↗
arXiv2011

Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass

We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a short-range model. We are therefore able to study both the mean-field and non-mean-field regimes. For one value of sigma, in the non-mean-field regime, we find evidence that the chiral glass transition temperature may be somewhat higher than the spin glass transition temperature. For the other values of sigma we see no evidence for this.

cond-mat.dis-nn↗
arXiv2010

Dynamics of Energy Transport in a Toda Ring

We present results on the relationships between persistent currents and the known conservation laws in the classical Toda ring. We also show that perturbing the integrability leads to a decay of the currents at long times, with a time scale that is determined by the perturbing parameter. We summarize several known results concerning the Toda ring in 1-dimension, and present new results relating to the frequency, average kinetic and potential energy, and mean square displacement in the cnoidal waves, as functions of the wave vector and a parameter that determines the non linearity.

cond-mat.stat-mech↗
arXiv2010

The de Almeida-Thouless line in vector spin glasses

We consider the infinite-range spin glass in which the spins have m > 1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is an Almeida Thouless (AT) line below which the "replica symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m, and verify our results by numerical simulations for m = 3$.

cond-mat.dis-nn↗
arXiv2010

Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions

We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By using a 3-spin spin-glass model with long-range power-law diluted interactions we are able to continuously tune the (effective) space dimension via the exponent of the interactions. Monte Carlo simulations of the spin-glass susceptibility and the two-point finite-size correlation length show that deep in the non-mean-field regime the finite-temperature transition is lost, whereas this is not the case in the mean-field regime, in agreement with the prediction of Moore and Drossel [Phys. Rev. Lett. 89, 217202 (2002)] that 3-spin models are in the same universality class as an Ising spin glass in a magnetic field. However, slightly in the non-mean-field region, we find an apparent transition in the 3-spin model, in contrast to results for the Ising spin glass in a field. This may indicate that even larger sizes are needed to probe the asymptotic behavior in this region.

cond-mat.dis-nn↗
arXiv2010

First order phase transition in the Quantum Adiabatic Algorithm

We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N we find that some instances have a discontinuous (first order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing N and may tend to 1 for N -> infinity.

cond-mat.stat-mech↗
arXiv2009

Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study larger sizes, 48x48x48, than have been attempted before at a spin glass phase transition. A finite-size scaling analysis indicates that the data is compatible with the most economical scenario: a common transition temperature for spins and chiralities.

cond-mat.dis-nn↗
arXiv2009

Continuum and lattice heat currents for oscillator chains

We show that two commonly used definitions for the heat current give different results--through the Kubo formula--for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of N particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by O(1/N). For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with O(1/N^eta) with 1 > eta > 0.5.

cond-mat.stat-mech↗
arXiv2009

Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally-applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that an Almeida-Thouless line only occurs in the mean field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.

cond-mat.dis-nn↗
arXiv2009

Information science and technology as applications of the physics of signalling

Adopting the scientific method a theoretical model is proposed as foundation for information science and technology, extending the existing theory of signaling: a fact f becomes known in a physical system only following the success of a test f, tests performed primarily by human sensors and applied to (physical) phenomena within which further tests may be performed. Tests are phenomena and classify phenomena. A phenomenon occupies both time and space, facts and inferences having physical counterparts which are phenomena of specified classes. Identifiers such as f are conventional, assigned by humans; a fact (f', f'') reports the success of a test of generic class f', the outcome f'' of the reported application classifying the successful test in more detail. Facts then exist only within structures of a form dictated by constraints on the structural design of tests. The model explains why responses of real time systems are not uniquely predictable and why restrictions, on concurrency in performing inferences within them, are needed. Improved methods, based on the model and applicable throughout the software life-cycle, are summarised in the paper. No report of similar work has been found in the literature.

cs.OH↗
arXiv2008

The Spin Glass Phase in the Four-State, Three-Dimensional Potts Model

We perform numerical simulations, including parallel tempering, on the Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the location of the transition and the value of the critical exponents. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the "random permutation" Potts glass.

cond-mat.dis-nn↗
arXiv2008

Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm

We study the typical (median) value of the minimum gap in the quantum version of the Exact Cover problem using Quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm (QAA) for much larger sizes than before. For a range of sizes, N <= 128, where the classical Davis-Putnam algorithm shows exponential median complexity, the QAA shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided crossing point of a Landau-Zener type (collision between the two lowest energy levels only).

cond-mat.dis-nn↗
arXiv2008

Large-scale Monte Carlo simulations of the three-dimensional XY spin glass

We study the XY spin glass by large-scale Monte Carlo simulations for sizes up to 24^3, down to temperatures below the transition temperature found in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes indicating that the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a very similar manner. We also address the optimal ratio of "over-relaxation" to "Metropolis" sweeps in the simulation.

cond-mat.dis-nn↗