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A. P. Young

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

At least 55 records · Page 3Linked to original sources
arXiv2008

New Insights from One-Dimensional Spin Glasses

The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial analysis. Thus it is of paramount importance to understand which predictions of the mean-field solution apply to non-mean-field systems, such as realistic short-range spin-glass models. The one-dimensional spin glass with random power-law interactions promises to be an ideal test-bed to answer this question: Not only can large system sizes-which are usually a shortcoming in simulations of high-dimensional short-range system-be studied, by tuning the power-law exponent of the interactions the universality class of the model can be continuously tuned from the mean-field to the short-range universality class. We present details of the model, as well as recent applications to some questions of the physics of spin glasses. First, we study the existence of a spin-glass state in an external field. In addition, we discuss the existence of ultrametricity in short-range spin glasses. Finally, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.

cond-mat.dis-nn↗
arXiv2007

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

We study the Heisenberg spin glass by large-scale Monte Carlo simulations for sizes up to 32^3, down to temperatures below the transition temperature claimed in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes, indicating the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a quite similar manner.

cond-mat.dis-nn↗
arXiv2006

Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study

We study the critical behavior of the short-range p-state Potts spin glass in three and four dimensions using Monte Carlo simulations. In three dimensions, for p = 3, a finite-size scaling analysis of the correlation length shows clear evidence of a transition to a spin-glass phase at T_c = 0.273(5) for a Gaussian distribution of interactions and T_c = 0.377(5) for a bimodal distribution. These results indicate that the lower critical dimension of the 3-state Potts glass is below three. By contrast, the correlation length of the ten-state (p = 10) Potts glass in three dimensions remains small even at very low temperatures and thus shows no sign of a transition. In four dimensions we find that the p = 3 Potts glass with Gaussian interactions has a spin-glass transition at T_c =0.536(3).

cond-mat.dis-nn↗
arXiv2006

Universality in three-dimensional Ising spin glasses: A Monte Carlo study

We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional spin glasses obey universality.

cond-mat.dis-nn↗
arXiv2005

Probing the Almeida-Thouless line away from the mean-field model

Results of Monte Carlo simulations of the one-dimensional long-range Ising spin glass with power-law interactions in the presence of a (random) field are presented. By tuning the exponent of the power-law interactions, we are able to scan the full range of possible behaviors from the infinite-range (Sherrington-Kirkpatrick) model to the short-range model. A finite-size scaling analysis of the correlation length indicates that the Almeida-Thouless line does not occur in the region with non-mean-field critical behavior in zero field. However, there is evidence that an Almeida-Thouless line does occur in the mean-field region.

cond-mat.dis-nn↗
arXiv2005

Degeneracy and Strong Fluctuation-Induced First-Order Phase Transition in the Dipolar Pyrochlore Antiferromagnet

We show that a continuous set of degenerate critical soft modes strongly enhances the first-order character of a fluctuation-induced first-order transition in the pyrochlore dipolar Heisenberg antiferromagnet. Such a degeneracy seems essential to explain the strong first-order transition recently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlo simulations and a perturbative renormalization group expansion.

cond-mat.mtrl-sci↗
arXiv2005

Defect energy of infinite-component vector spin glasses

We compute numerically the zero temperature defect energy, Delta E, of the vector spin glass in the limit of an infinite number of spin components m, for a range of dimensions 2 <= d <= 5. Fitting to Delta E ~ L^theta, where L is the system size, we obtain: theta = -1.54 (d=2), theta = -1.04 (d=3), theta = -0.67 (d=4) and theta = -0.37 (d=5). These results show that the lower critical dimension, d_l (the dimension where theta changes sign), is significantly higher for m=infinity than for finite m (where 2 < d_l < 3).

cond-mat.dis-nn↗
arXiv2005

Temperature Cycles in the Heisenberg Spin Glass

We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the timescale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that `full' rejuvenation can be observed in experiments even if temperature chaos is absent.

cond-mat.dis-nn↗
arXiv2004

Finite size scaling of the correlation length above the upper critical dimension

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a hypothesis that FSS expressions in dimension d greater than the upper critical dimension of 4 should have L replaced by L^{d/4} for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in d = 4.

cond-mat.dis-nn↗
arXiv2004

Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses

We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast to the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.

cond-mat.dis-nn↗
arXiv2004

Free energies in the presence of electric and magnetic fields

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions.

cond-mat.stat-mech↗
arXiv2004

Spin glasses in the limit of an infinite number of spin components

We consider the spin glass model in which the number of spin components, m, is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi long range order" below the transition temperature. We also show that the spin glass transition temperature is zero in three dimensions.

cond-mat.dis-nn↗
arXiv2004

Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions

We study the correlation length of the two-dimensional Ising spin glass with a Gaussian distribution of interactions, using an efficient Monte Carlo algorithm proposed by Houdayer, that allows larger sizes and lower temperatures to be studied than was possible before. We find that the "effective" value of the bulk correlation length exponent νincreases as the temperature is lowered, and, at low temperatures, apparently approaches -1/θ, where θ~ -0.29 is the stiffness exponent obtained at zero temperature. This means scaling is satisfied and earlier results at higher temperatures that find a smaller value for νare affected by corrections to scaling.

cond-mat.dis-nn↗
arXiv2004

Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering.

cond-mat.dis-nn↗
arXiv2003

Aging Dynamics of the Heisenberg Spin Glass

We numerically study the non-equilibrium dynamics of the three dimensional Heisenberg Edwards-Anderson spin glass following a sudden quench to its low temperature phase. The subsequent aging behavior of the system is analyzed in detail, and the scaling behavior of various space-time correlation functions is investigated for both spin and chiral degrees of freedom. We carefully compare our results with those obtained from simulations of the more studied Ising version of the model, and with experiments on real spin glasses in which the spins have vectorial character. Finally, the present dynamical study offers new perspectives into the possibility of spin-chirality decoupling at low temperature in vectorial spin glasses.

cond-mat.dis-nn↗
arXiv2003

Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions

Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both finite-temperature and ground-state studies are carried out. For the range of sizes studied the data cannot be fitted to any of the standard spin-glass scenarios without including corrections to scaling. Incorporating such corrections we find that the fractal dimension of the surface of the excitations, is either equal to the space dimension, consistent with replica symmetry breaking, or very slightly less than it. The latter case is consistent with the droplet and "trivial-nontrivial" (TNT) pictures.

cond-mat.dis-nn↗
arXiv2003

Time and length scales in spin glasses

We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three dimensional Heisenberg spin glass.

cond-mat.dis-nn↗