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Thomas Jorg

Publications and source records attributed to Thomas Jorg.

13 recordsLinked to original sources
arXiv2012

Ultrametric probe of the spin-glass state in a field

We study the ultrametric structure of phase space of one-dimensional Ising spin glasses with random power-law interaction in an external random field. Although in zero field the model in both the mean-field and non-mean-field universality classes shows an ultrametric signature [Phys. Rev. Lett. 102, 037207 (2009)], when a field is applied ultrametricity seems only present in the mean-field regime. The results for the non-mean field case in an external field agree with data for spin glasses studied within the Migdal-Kadanoff approximation. Our results therefore suggest that the spin-glass state might be fragile to external fields below the upper critical dimension.

cond-mat.dis-nn↗
arXiv2011

The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow

The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal-Kadanoff renormalization group. We see, in particular, how these properties are connected with the presence of a cascade of fixed points in the renormalization group flow. Of particular interest are two unstable fixed points that correspond to two different spin-glass phases at zero temperature. We discuss how these phenomena are related with the presence of entropy fluctuations and temperature chaos, and universality in this model.

cond-mat.dis-nn↗
arXiv2009

Quantum Annealing of Hard Problems

Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems for which the efficiency can be studied analytically using techniques based on the statistical mechanics of spin glasses.

quant-ph↗
arXiv2009

Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings

We study link-diluted $\pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.

cond-mat.dis-nn↗
arXiv2008

Evidence for universal scaling in the spin-glass phase

We perform Monte Carlo simulations of Ising spin-glass models in three and four dimensions, as well as of Migdal-Kadanoff spin glasses on a hierarchical lattice. Our results show strong evidence for universal scaling in the spin-glass phase in all three models. Not only does this allow for a clean way to compare results obtained from different coupling distributions, it also suggests that a so far elusive renormalization group approach within the spin-glass phase may actually be feasible.

cond-mat.dis-nn↗
arXiv2008

Simple Glass Models and their Quantum Annealing

We study first order quantum phase transitions in mean-field spin glasses. We solve the quantum Random Energy Model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all `Random First Order' models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.

quant-ph↗
arXiv2008

Behavior of Ising Spin Glasses in a Magnetic Field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field--temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.

cond-mat.dis-nn↗
arXiv2007

Comment on "Ultrametricity in the Edwards-Anderson Model"

In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex ultrametric structure similar to the one described by the replica symmetry breaking solution of the mean field model. We illustrate by numerical simulations that the relations used by Contucci {\it et al.} as evidence for an ultrametric structure in the 3d EA model are fulfilled to similar accuracy in the two-dimensional EA model, which is well-described by the droplet picture and has no spin glass phase at finite temperature. We conclude that the data presented in the Contucci {\it et al.} Letter is not sufficient to dismiss the possibility that, e.g., the droplet model might describe the behavior of the 3d EA model.

cond-mat.dis-nn↗
arXiv2007

Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and Universality

We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p*, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.

cond-mat.dis-nn↗
arXiv2004

Cluster Monte Carlo algorithms for diluted spin glasses

Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin glass transition temperature. The application of such algorithms to the site-diluted EA model in three dimensions is discussed and the efficiency of the two algorithms is compared among each other and to parallel tempering. Finally, we give evidence for a spin glass transition in the three-dimensional site-diluted EA model with Gaussian couplings at a site occupation of p = 62.5 %.

cond-mat.dis-nn↗
arXiv2003

Quenched spectroscopy with fixed-point and chirally improved fermions

We present results from quenched spectroscopy calculations with the parametrized fixed-point and the chirally improved Dirac operators. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. This allows us to work at small quark masses and we explore pseudoscalar-mass to vector-mass ratios down to 0.28. We discuss meson and baryon masses, their scaling properties, finite volume effects and compare our results with recent large scale simulations. We find that the size of quenching artifacts of the masses is strongly correlated with their experimentally observed widths and that the gauge and hadronic scales are consistent.

hep-lat↗
arXiv2002

Chiral measurements in quenched lattice QCD with Fixed Point fermions

We construct a parametrization of a Fixed Point (FP) Dirac operator and apply it in quenched lattice QCD. The symmetry requirements for a general lattice Dirac operator are discussed and an efficient way to make a practical construction of general lattice Dirac operators is provided. We use such a lattice Dirac operator to approximately solve the Renormalization Group equation that defines the FP Dirac operator in an iterative procedure. We discuss the properties of this parametrization and show that its breaking of chiral symmetry and its scaling violations in hadron specroscopy are much reduced compared to the Wilson Dirac operator. Furthermore, we discuss the overlap construction with the parametrized FP Dirac operator and its properties. Using the Atiyah-Singer index theorem, a consequence of chiral symmetry, we calculate the quenched topological susceptibility. Finally, we determine the renormalized low-energy constant Sigma of quenched Chiral Perturbation Theory using a finite volume scaling technique.

hep-lat↗