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Bernd A. Berg

Publications and source records attributed to Bernd A. Berg.

At least 55 records · Page 3Linked to original sources
arXiv2006

Glauber dynamics of phase transitions: SU(3) lattice gauge theory

Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory notation, i.e., cooling of the spin systems). In the present paper we set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects by comparing to equilibrium results at first and second order phase transition temperatures, obtained by re-weighting from a multicanonical ensemble. Our finding is that the dynamics entirely overwhelms the critical and non-critical equilibrium effects. In the second half of the paper we extend our results by investigating the Glauber dynamics of pure SU(3) lattice gauge on $N_τ N_σ^3$ lattices directly under heating quenches from the confined into the deconfined regime. The exponential growth factors of the initial response are calculated, which give Debye screening mass estimates. The quench leads to competing vacuum domains of distinct $Z_3$ triality, which delay equilibration of pure gauge theory forever, while their role in full QCD remains a subtle question. As in spin systems we find for pure SU(3) gauge theory a dynamical growth of structure factors, reaching maxima which scale approximately with the volume of the system, before settling down to equilibrium. Their influence on various observables is studied and different lattice sizes are simulated to illustrate an approach to a finite volume continuum limit. Strong correlations are found during the dynamical process, but not in the deconfined phase at equilibrium.

hep-lat↗
arXiv2005

Biased Metropolis-Heat-Bath Algorithm for Fundamental-Adjoint SU(2) Lattice Gauge Theory

For SU(2) lattice gauge theory with the fundamental-adjoint action an efficient heat-bath algorithm is not known so that one had to rely on Metropolis simulations supplemented by overrelaxation. Implementing a novel biased Metropolis-heat-bath algorithm for this model, we find improvement factors in the range 1.45 to 2.06 over conventionally optimized Metropolis simulations. If one optimizes further with respect to additional overrelaxation sweeps, the improvement factors are found in the range 1.3 to 1.8.

hep-lat↗
arXiv2005

Rugged Metropolis Sampling with Simultaneous Updating of Two Dynamical Variables

The Rugged Metropolis (RM) algorithm is a biased updating scheme, which aims at directly hitting the most likely configurations in a rugged free energy landscape. Details of the one-variable (RM$_1$) implementation of this algorithm are presented. This is followed by an extension to simultaneous updating of two dynamical variables (RM$_2$). In a test with Met-Enkephalin in vacuum RM$_2$ improves conventional Metropolis simulations by a factor of about four. Correlations between three or more dihedral angles appear to prevent larger improvements at low temperatures. We also investigate a multi-hit Metropolis scheme, which spends more CPU time on variables with large autocorrelation times.

cond-mat.stat-mech↗
arXiv2005

Heat Bath Efficiency with Metropolis-Type Updating

We illustrate for 4D SU(2) and U(1) lattice gauge theory that sampling with a biased Metropolis scheme is essentially equivalent to using the heat bath algorithm. Only, the biased Metropolis method can also be applied when an efficient heat bath algorithm does not exist.

hep-lat↗
arXiv2004

Model A Dynamics and the Deconfining Phase Transition for Pure Lattice Gauge Theory

We consider model A dynamics for a heating quench from the disordered (confined) into the ordered (deconfined) phase of SU(3) lattice gauge theory. For $4 N_σ^3$ lattices the exponential growth factors of low-lying structure function modes are calculated. The linear theory of spinodal decompositions is compared with the data from an effective model and the Debye screening mass is estimated from the critical mode. Further, the quench leads to competing vacuum domains, which make the equilibration of the QCD vacuum after the heating non-trivial. We investigate the influence of such domains on the gluonic energy density.

hep-lat↗
arXiv2004

Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations

Treating realistically the ambient water is one of the main difficulties in applying Monte Carlo methods to protein folding. The solvent-accessible area method, a popular method for treating water implicitly, is investigated by means of Metropolis simulations of the brain peptide Met-Enkephalin. For the phenomenological energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied that had been proposed by previous authors. The simulations are compared with each other, with simulations with a distance dependent electrostatic permittivity $ε(r)$, and with vacuum simulations ($ε=2$). Parallel tempering and a recently proposed biased Metropolis technique are employed and their performances are evaluated. The measured observables include energy and dihedral probability densities (pds), integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other sets, selected configurations are minimized in search of the global energy minima. Unique minima are found for the vacuum and the $ε(r)$ system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, autocorrelation times vary dramatically with the ASP parameters. Three ASP sets have much smaller autocorrelations at 300 K than the vacuum simulations, opening the possibility that simulations can be speeded up vastly by judiciously chosing details of the force

cond-mat.soft↗
arXiv2004

Dynamics of Phase Transitions: The 3D 3-state Potts model

In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model, which serves as an effective model for some QCD properties. We investigate the linear theory of spinodal decomposition in some detail. It describes the early time evolution of the 3D model under a quench from the disordered into the ordered phase well, but fails in 2D. Further, the quench leads to competing vacuum domains, which are difficult to equilibrate, even in the presence of a small external magnetic field. From our hysteresis study we find, as before, a dynamics dominated by spinodal decomposition. There is evidence that some effects survive in the case of a cross-over. But the infinite volume extrapolation is difficult to control, even with lattices as large as $120^3$.

hep-lat↗
arXiv2003

Dynamics of Phase Transitions by Hysteresis Methods I

In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.

hep-lat↗
arXiv2003

Indications for Criticality at Zero Curvature in a 4d Regge Model of Euclidean Quantum Gravity

We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent parameters. We determine the zero curvature, $ =0$, line in the coupling constant plane by numerical simulations. When crossing this line we find a strong, probably first order, phase transition line with indications of a second order endpoint. Beyond the endpoint the transition through the $ =0$ line appears to be a crossover. Previous investigations, using the Regge or the Dynamical Triangulation approach, dealt with a limit in which the first order transition prevails.

hep-lat↗
arXiv2003

Biased Metropolis Sampling for Rugged Free Energy Landscapes

Metropolis simulations of all-atom models of peptides (i.e. small proteins) are considered. Inspired by the funnel picture of Bryngelson and Wolyness, a transformation of the updating probabilities of the dihedral angles is defined, which uses probability densities from a higher temperature to improve the algorithmic performance at a lower temperature. The method is suitable for canonical as well as for generalized ensemble simulations. A simple approximation to the full transformation is tested at room temperature for Met-Enkephalin in vacuum. Integrated autocorrelation times are found to be reduced by factors close to two and a similar improvement due to generalized ensemble methods enters multiplicatively.

cond-mat.stat-mech↗
arXiv2003

Metropolis simulations of Met-Enkephalin with solvent-accessible area parameterizations

We investigate the solvent-accessible area method by means of Metropolis simulations of the brain peptide Met-Enkephalin at 300$ K$. For the energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied. The simulations are compared with one another, with simulations with a distance dependent electrostatic permittivity $ε(r)$, and with vacuum simulations ($ε=2$). Parallel tempering and the biased Metropolis techniques RM$_1$ are employed and their performance is evaluated. The measured observables include energy and dihedral probability densities (pds), integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other systems selected configurations are minimized in search of the global energy minima, which are found for the vacuum and the $ε(r)$ system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, we find three ASP sets for which the autocorrelations at 300$ $K are considerably smaller than for vacuum simulations.

cond-mat.stat-mech↗
arXiv2003

Metropolis Importance Sampling for Rugged Dynamical Variables

A funnel transformation is introduced, which acts recursively from higher towards lower temperatures. It biases the a-priori probabilities of a canonical or generalized ensemble Metropolis simulation, so that they zoom in on the global energy minimum, if a funnel exists indeed. A first, crude approximation to the full transformation, called rugged Metropolis one (RM$_1$), is tested for Met-Enkephalin. At 300$ $K the computational gain is a factor of two and, due to its simplicity, RM$_1$ is well suited to replace the conventional Metropolis updating for these kind of systems.

cond-mat.soft↗
arXiv2002

Dynamics of the 2d Potts model phase transition

The dynamics of 2d Potts models, which are temperature driven through the phase transition using updating procedures in the Glauber universality class, is investigated. We present calculations of the hysteresis for the (internal) energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used to define finite volume estimators of physical observables, which can be used to study the approach to the infinite volume limit. We compare with equilibrium configurations and the preliminary indications are that the dynamics leads to considerable alterations of the statistical properties of the configurations studied.

hep-lat↗
arXiv2002

Multicanonical Simulations Step by Step

The purpose of this article is to provide a starter kit for multicanonical simulations in statistical physics. Fortran code for the $q$-state Potts model in $d=2, 3,...$ dimensions can be downloaded from the Web and this paper describes simulation results, which are in all details reproducible by running prepared programs. To allow for comparison with exact results, the internal energy, the specific heat, the free energy and the entropy are calculated for the $d=2$ Ising ($q=2$) and the $q=10$ Potts model. % in a temperature range from $T=\infty$ down to sufficiently low % temperatures, such that the groundstates are included in the sampling. Analysis programs, relying on an all-log jackknife technique, which is suitable for handling sums of very large numbers, are introduced to calculate our final estimators.

cond-mat↗
arXiv2002

Generalized Ensemble Simulations for Complex Systems

The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the simulation. Although not realized by nature, these ensembles can be implemented on computers. In recent years generalized ensembles have in particular been studied for the simulation of complex systems. For these systems it is typical that conflicting constraints lead to free energy barriers, which fragment the configuration space. Examples of major interest are spin glasses and proteins. In my overview I first comment on the strengths and weaknesses of a few major approaches, multicanonical simulations, transition variable methods, and parallel tempering. Subsequently, two applications are presented: a new analysis of the Parisi overlap distribution for the 3d Edwards-Anderson Ising spin glass and the helix-coil transition of amino-acid homo-oligomers.

cond-mat.stat-mech↗
arXiv2002

Overlap Distribution of the Three-Dimensional Ising Model

We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multi-overlap MC algorithm. Below the critical temperature interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.

cond-mat.stat-mech↗