arXiv subjects

B. A. Berg

Publications and source records attributed to B. A. Berg.

15 recordsLinked to original sources

arXiv2012

Density of states and Fisher's zeros in compact U(1) pure gauge theory

We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U(1) on 4^4, 6^4 and 8^4 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition function in the complex beta=1/g^2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher's zeros, the width and depth of the plaquette distribution at the value of beta where the two peaks have equal height. We discuss strategies to discriminate between first and second order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.

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↗

arXiv2003

Multi-Overlap Simulations for Transitions between Reference Configurations

We introduce a new procedure to construct weight factors, which flatten the probability density of the overlap with respect to some pre-defined reference configuration. This allows one to overcome free energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brainpeptide Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free energy barrier.

cond-mat.stat-mech↗

arXiv2000

Spectrum of the U(1) staggered Dirac operator in four dimensions

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.

hep-lat↗

arXiv2000

Universality and Chaos in Quantum Field Theories

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution, $P(s)$. We further study two-color QCD at nonzero chemical potential, $μ$, by constructing the spacing distribution of adjacent eigenvalues in the complex plane. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior.

hep-lat↗

arXiv1998

Quantum Chaos in Compact Lattice QED

Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.

hep-lat↗

arXiv1996

Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times 2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the $β$-function of pure gauge theory and conclude that a physical limit through scaling is possible.

hep-lat↗

arXiv1995

Static Quark Potentials in Quantum Gravity

We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. The action consists of the gravitational term given by Regge's discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants $m_{p}^{2}$ and $β$ respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.

hep-lat↗

arXiv1994

SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.

hep-lat↗

arXiv1992

Multicanonical Study of the 3D Ising Spin Glass

We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite size scaling, as well as the zero temperature limit to explore the ground state properties.

cond-mat↗

arXiv1992

Multicanonical Spin Glass Simulations

We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass model within the recently introduced multicanonical ensemble. Replica on lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate is found, we are able to give a lower bound on the number of statistically independent groundstates sampled. Temperature dependence of the energy, entropy and other quantities of interest are easily calculable. In particular we report the groundstate results. Computations involving the spin glass order parameter are more tedious. Our data indicate that the large $L$ increase of the ergodicity time is reduced to an approximately $V^3$ power law. Altogether the results suggest that the multicanonical ensemble improves the situation of simulations for spin glasses and other systems which have to cope with similar problems of conflicting constraints.

hep-lat↗

arXiv1992

Recent Results of Multimagnetical Simulations of the Ising Model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension.

hep-lat↗

arXiv1992

Properties of Interfaces in the two and three dimensional Ising Model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^μ$ to be $F^s_0 = 1.52 \pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.

hep-lat↗

arXiv1992

Multimagnetical Simulations

We modified the recently proposed multicanonical MC algorithm for the case of a magnetic field driven order--order phase transition. We test this {\it multimagnetic} Monte Carlo algorithm for the D=2 Ising model at $β=0.5$ and simulate square lattices up to size $100 \times 100$. On these lattices with periodic boundary conditions it is possible to enhance the appearance of order-order interfaces during the simulation by many orders of magnitude as compared to the standard Monte Carlo simulation.

hep-lat↗

arXiv1992

Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions

Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes $100\times100$. It is demonstrated that the new algorithm $lacks$ an exponentially fast increase of the tunneling time between metastable states as a function of the linear size $L$ of the system. Instead, the tunneling time diverges approximately proportional to $L^{2.65}$. Thus the computational effort as counted per degree of freedom for generating an independent configuration in the unstable region of the model rises proportional to $V^{2.3}$, where $V$ is the volume of the system. On our largest lattice we gain more than two orders of magnitude as compared to a standard heat bath algorithm. As a first physical application we report a high precision computation of the interfacial tension.

hep-lat↗