arXiv subjects

Bernd A. Berg

Publications and source records attributed to Bernd A. Berg.

At least 37 records · Page 2Linked to original sources

arXiv2009

Deconfining phase transition on a double-layered torus

Deconfined regions in relativistic heavy ion collisions are limited to small volumes surrounded by a confined exterior. Here the geometry of a double layered torus is discussed, which allows for different temperatures in its two layers. This geometry enables one to approach the QCD continuum limit for small deconfined volumes with confined exteriors in a more realistic fashion than by using periodic boundary conditions. Preliminary data from a study for pure SU(3) lattice gauge theory support a substantial increase in a pseudo transition temperature.

hep-lat↗

arXiv2009

Fortran MPI Checkerboard Code for SU(3) Lattice Gauge Theory II

We study the performance of MPI checkerboard code for SU(3) lattice gauge theory as function of the number of MPI processes, which run in parallel on an identical number of CPU cores. Computing platforms explored are a small PC cluster at FSU and the Cray at NERSC.

hep-lat↗

arXiv2009

Fortran MPI Checkerboard Code for SU(3) Lattice Gauge Theory I

We document Fortran MPI checkerboard code for Markov Chain Monte Carlo simulations of pure SU(3) lattice gauge theory with the Wilson action on a D-dimensional double-layered torus. This includes the usual torus with periodic boundary conditions as an optional case. We use Cabibbo-Marinari heatbath checkerboard updating. Parallelization on sublattices is implemented in all D directions and can be restricted to less than D directions. The parallelization techniques of this paper can be used for any model with interactions of link variables defined on plaquettes.

hep-lat↗

arXiv2009

Program package for multicanonical simulations of U(1) lattice gauge theory

We document our Fortran 77 code for multicanonical simulations of 4D U(1) lattice gauge theory in the neighborhood of its phase transition. This includes programs and routines for canonical simulations using biased Metropolis heatbath updating and overrelaxation, determination of multicanonical weights via a Wang-Landau recursion, and multicanonical simulations with fixed weights supplemented by overrelaxation sweeps. Measurements are performed for the action, Polyakov loops and some of their structure factors. Many features of the code transcend the particular application and are expected to be useful for other lattice gauge theory models as well as for systems in statistical physics.

hep-lat↗

arXiv2008

Phase Transition Properties of 3D Potts Models

Using multicanonical Metropolis simulations we estimate phase transition properties of 3D Potts models for q=4 to 10: The transition temperatures, latent heats, entropy gaps, normalized entropies at the disordered and ordered endpoints, interfacial tensions, and spinodal endpoints.

hep-lat↗

arXiv2008

Thermodynamics of two lattice ice models in three dimensions

In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for groundstate configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.

cond-mat.stat-mech↗

arXiv2008

Thermalization in SU(3) gauge theory after a deconfining quench

We determine the time evolution of fluctuations of the Polyakov loop after a quench into the deconfined phase of SU(3) gauge theory from a simple classical relativistic Lagrangian. We compare the structure factors, which indicate spinodal decomposition followed by relaxation, to those obtained via Markov Chain Monte Carlo techniques in SU(3) lattice gauge theory. We find that the time when the structure factor peaks diverges like $\sim 1/k^2$ in the long-wavelength limit. This is due to formation of competing Z(3) domains for configurations where the Polyakov loop exhibits non-perturbatively large variations in space, which delay thermalization of long wavelength modes. For realistic temperatures, and away from the extreme weak-coupling limit, we find that even modes with $k$ on the order of $T$ experience delayed thermalization. Relaxation times of very long wavelength modes are found to be on the order of the size of the system; thus, the dynamics of competing domains should accompany the hydrodynamic description of the deconfined vacuum.

hep-ph↗

arXiv2008

Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory

We study Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase conversion in finite volumes. For the conversion time we find the relationship $τ_{\rm con} = τ_{\rm nu} [1+f_d(q)]$. Here $d$ is the space dimension, $τ_{\rm nu}$ the nucleation time in the volume $V$, and $f_d(q)$ a scaling function. Its dimensionless argument is $q=τ_{\rm ex}/ τ_{\rm nu}$, where $τ_{\rm ex}$ is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate $f_d(q)$ in one, two and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for $f_d(q)$.

cond-mat.stat-mech↗

arXiv2007

From Data to Probability Densities without Histograms

When one deals with data drawn from continuous variables, a histogram is often inadequate to display their probability density. It deals inefficiently with statistical noise, and binsizes are free parameters. In contrast to that, the empirical cumulative distribution function (obtained after sorting the data) is parameter free. But it is a step function, so that its differentiation does not give a smooth probability density. Based on Fourier series expansion and Kolmogorov tests, we introduce a simple method, which overcomes this problem. Error bars on the estimated probability density are calculated using a jackknife method. We give several examples and provide computer code reproducing them. You may want to look at the corresponding figures 4 to 9 first.

physics.data-an↗

arXiv2007

SU(3) Deconfining Phase Transition in a Box with Cold Boundaries

Deconfined regions created in heavy ion collisions are bordered by the confined phase. We discuss boundary conditions (BCs) to model a cold exterior. Monte Carlo simulations of pure SU(3) lattice gauge theory with thus inspired BCs show scaling. Corrections to usual results survive in the finite volume continuum limit and we estimate them in a range from L=5-10 fermi as function of the volume size $L^3$. In magnitude these corrections are comparable to those obtained by including quarks.

hep-lat↗

arXiv2007

Numerical calculation of the combinatorial entropy of partially ordered ice

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for many other systems.

cond-mat.stat-mech↗

arXiv2007

Markov-Chain Monte Carlo Methods for Simulations of Biomolecules

The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of the importance of computer simulations. Major enabling techniques are Markov Chain Monte Carlo (MCMC) and Molecular Dynamics (MD) simulations. This article deals with the MCMC approach. First basic simulation techniques, as well as methods for their statistical analysis are reviewed. Afterwards the focus is on generalized ensembles and biased updating, two advanced techniques, which are of relevance for simulations of biomolecules, or are expected to become relevant with that respect. In particular we consider the multicanonical ensemble and the replica exchange method (also known as parallel tempering or method of multiple Markov chains).

cond-mat.stat-mech↗

arXiv2007

Deconfining Phase Transition on Lattices with Boundaries at Low Temperature

In lattice gauge theory (LGT) equilibrium simulations of QCD are usually performed with periodic boundary conditions (BCs). In contrast to that deconfined regions created in heavy ion collisions are bordered by the confined phase. Here we discuss BCs in LGT, which model a cold exterior of the lattice volume. Subsequently we perform Monte Carlo (MC) simulations of pure SU(3) LGT with a thus inspired simple change of BCs using volumes of a size comparable to those typically encountered in the BNL relativistic heavy ion collider (RHIC) experiment. Corrections to the usual LGT results survive in the finite volume continuum limit and we estimate them as function of the volume size. In magnitude they are found comparable to those of including quarks. As observables we use a pseudocritical temperature, which rises opposite to the effect of quarks, and the width of the transition, which broadens similar to the effect of quarks.

hep-lat↗

arXiv2007

Normalized entropy density of the 3D 3-state Potts model

Using a multicanonical Metropolis algorithm we have performed Monte Carlo simulations of the 3D 3-state Potts model on $L^3$ lattices with L=20, 30, 40, 50. Covering a range of inverse temperatures from $β_{\min}=0$ to $β_{\max}=0.33$ we calculated the infinite volume limit of the entropy density $s(β)$ with its normalization obtained from $s(0)=\ln 3$. At the transition temperature the entropy and energy endpoints in the ordered and disordered phase are estimated employing a novel reweighting procedure. We also evaluate the transition temperature and the order-disorder interface tension. The latter estimate increases when capillary waves are taken into account.

hep-lat↗

arXiv2007

Residual Entropy of Ordinary Ice from Multicanonical Simulations

We introduce two simple models with nearest neighbor interactions on 3D hexagonal lattices. Each model allows one to calculate the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. This gives the correction to the residual entropy derived by Linus Pauling in 1935. Our estimate is found to be within less than 0.1% of an analytical approximation by Nagle, which is an improvement of Pauling's result. We pose it as a challenge to experimentalists to improve on the accuracy of a 1936 measurement by Giauque and Stout by about one order of magnitude, which would allow one to identify corrections to Pauling's value unambiguously. It is straightforward to transfer our methods to other crystal systems.

cond-mat.stat-mech↗

arXiv2006

Wang-Landau/Multibondic Cluster Simulations for Second-Order Phase Transitions

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau/multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach two orders of magnitude.

cond-mat.stat-mech↗

arXiv2006

Non-Perturbative U(1) Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_τ N_s^3$ lattices for $N_τ$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_τ=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_τ$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.

hep-lat↗

arXiv2006

Critical Exponents for U(1) Lattice Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_τ N_s^3$ lattices for $N_τ$ fixed and $N_s\to\infty$, approaching the phase transition from the confined phase. For $N_τ=4$, 5 and 6 our data contradict the expected scenario that this transition is either first order or in the universality class of the 3d XY model. If there are no conceptional flaws in applying the argument that the Gaussian fixed point in 3d is unstable to our systems, estimates of the critical exponents $α/ν$, $γ/ν$, $(1-β)/ν$ and $2-η$ indicate the existence of a new, non-trivial renormalization group fixed point for second order phase transitions in 3d. Such a fixed point would be of importance for renormalization group theory and statistical physics.

hep-lat↗