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W. Kerler

Publications and source records attributed to W. Kerler.

At least 19 recordsLinked to original sources
arXiv2007

Modified SO(3) Lattice Gauge Theory at non zero T with Parallel Tempering: Monopole and Vortex Condensation

The deconfinement transition is studied close to the continuum limit of SO(3) lattice gauge theory. High barriers for tunnelling among different twist sectors causing loss of ergodicity for local update algorithms are circumvented by means of parallel tempering. We compute monopole and center vortex free energies both within the confining phase and through the deconfinement transition. We discuss in detail the general problem of defining order parameters for adjoint actions.

hep-lat↗
arXiv2006

Vortex free energy and deconfinement in center-blind discretizations of Yang-Mills theories

Maximal 't Hooft loops are studied in SO(3) lattice gauge theory at finite temperature T. Tunneling barriers among twist sectors causing loss of ergodicity for local update algorithms are overcome through parallel tempering, enabling us to measure the vortex free energy F and to identify a deconfinement transition at some $β_A^{crit}$. The behavior of F below $β_A^{crit}$ shows however striking differences with what is expected from discretizations in the fundamental representation.

hep-th↗
arXiv2005

Probing the Aoki phase with N_f=2 Wilson fermions at finite temperature

In this letter we report on a numerical investigation of the Aoki phase in the case of finite temperature which continues our former study at zero temperature. We have performed simulations with Wilson fermions at $β=4.6$ using lattices with temporal extension $N_τ=4$. In contrast to the zero temperature case, the existence of an Aoki phase can be confirmed for a small range in $κ$ at $β=4.6$, however, shifted slightly to lower $κ$. Despite fine-tuning $κ$ we could not separate the thermal transition line from the Aoki phase.

hep-lat↗
arXiv2004

A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\barψ i γ_{5} τ^{3}ψ$ was added to the fermion action. The order parameter $<\barψ i γ_{5}τ^{3}ψ>$ was computed with the Hybrid Monte Carlo algorithm at several values of $(β,κ,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $β=4.0$ and 4.3, while we do not find parity-flavor breaking at $β=4.6$ and 5.0.

hep-lat↗
arXiv2003

The Aoki phase for N_f=2 Wilson fermions revisited

We report on a numerical reinvestigation of the Aoki phase in full lattice QCD with two flavors of unimproved Wilson fermions. For zero temperature the Aoki phase can be confirmed at inverse coupling $β=4.0$ and $β=4.3$, but not at $β=4.6$ and $β=5.0$. At non-zero temperature the Aoki phase was found to exist also at $β=4.6$.

hep-lat↗
arXiv2002

Parallel tempering in full QCD with Wilson fermions

We study the performance of QCD simulations with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering on $10^4$ and $12^4$ lattices. In order to compare tempered with standard simulations, covariance matrices between sub-ensembles have to be formulated and evaluated using the general properties of autocorrelations of the parallel tempering algorithm. We find that rendering the hopping parameter $κ$ dynamical does not lead to an essential improvement. We point out possible reasons for this observation and discuss more suitable ways of applying parallel tempering to QCD.

hep-lat↗
arXiv1998

Properties of U(1) lattice gauge theory with monopole term

In 4D compact U(1) lattice gauge theory with a monopole term added to the Wilson action we first reveal some properties of a third phase region at negative $β$. Then at some larger values of the monopole coupling $λ$ by a finite-size analysis we find values of the critical exponent $ν$ close to, however, different from the Gaussian value.

hep-lat↗
arXiv1998

Phase structure of U(1) lattice gauge theory with monopole term

We investigate four-dimensional compact U(1) lattice gauge theory with a monopole term added to the Wilson action. First we consider the phase structure at negative $β$, revealing some properties of a third phase region there, in particular the existence of a number of different states. Then our present studies concentrate on larger values of the monopole coupling $λ$ where the confinement-Coulomb phase transition turns out to become of second order. Performing a finite-size analysis we find that the critical exponent $ν$ is close to, however, different from the gaussian value and that in the range considered $ν$ increases somewhat with $λ$.

hep-lat↗
arXiv1998

Gluon propagator and zero-momentum modes in SU(2) lattice gauge theory

We investigate propagators in Lorentz (or Landau) gauge by Monte Carlo simulations. In order to be able to compare with perturbative calculations we use large $β$ values. There the breaking of the Z(2) symmetry turns out to be important for all of the four lattice directions. Therefore we make sure that the analysis is performed in the correct state. We discus implications of the gauge fixing mechanism and point out the form of the weak-coupling behavior to be expected in the presence of zero-momentum modes. Our numerical result is that the gluon propagator in the weak-coupling limit is strongly affected by zero-momentum modes. This is corroborated in detail by our quantitative comparison with analytical calculations.

hep-lat↗
arXiv1997

Gluon propagator and zero-momentum modes on the lattice

We investigate the propagators of 4D SU(2) gauge theory in Landau gauge by Monte Carlo simulations. To be able to compare with perturbative calculations we use large $β$ values. There the breaking of the Z(2) symmetry causes large effects for all four lattice directions and doing the analysis in the appropriate state gets important. We find that the gluon propagator in the weak-coupling limit is strongly affected by zero-momentum modes.

hep-lat↗
arXiv1997

Critical exponents in U(1) lattice gauge theory with a monopole term

We investigate critical properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term for values of the monopole coupling $λ$ such that the transition is of second order. It has been previously shown that at $λ= 0.9$ the critical exponent is already characteristic of a second-order transition and that it is different from the one of the Gaussian case. In the present study we perform a finite size analysis at $λ=1.1$ to get information wether the value of this exponent is universal.

hep-lat↗
arXiv1997

Monopoles and deconfinement transition in SU(2) lattice gauge theory

We investigate SU(2) lattice gauge theory in four dimensions in the maximally abelian projection. Studying the effects on different lattice sizes we show that the deconfinement transition of the fields and the percolation transition of the monopole currents in the three space dimensions are precisely related. To arrive properly at this result the uses of a mathematically sound characterization of the occurring networks of monopole currents and of an appropriate method of gauge fixing turn out to be crucial. In addition we investigate detailed features of the monopole structure in time direction.

hep-lat↗
arXiv1996

Critical properties and monopoles in U(1) lattice gauge theory

We present a detailed study of the properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term, for values of the monopole coupling $λ$ such that the transition is of second order. By a finite size analysis we show that at $λ= 0.9$ the critical exponent is already characteristic of a second-order transition. Moreover, we find that this exponent is definitely different from the one of the Gaussian case. We further observe that the monopole density becomes approximately constant in the second-order region. Finally we reveal the unexpected phenomenon that the phase transition persists up to very large values of $λ$, where the transition moves to (large) negative $β$.

hep-lat↗
arXiv1996

Critical behavior and monopole density in U(1) lattice gauge theory

Our study of the energy distribution has shown that the strength of the first order transition in the four-dimensional compact U(1) lattice gauge theory decreases when the coupling $λ$ of the monopole term increases. The disappearance of the energy gap for sufficiently large values of $λ$ indicates that the transition ultimately becomes of second order. In our present investigation, based on a finite-size analysis, we show that already at $λ= 0.9$ the critical exponent is characteristic of a second-order transition. Interestingly, this exponent turns out to be definitely different from that of the Gaussian case. We observe that the monopole density becomes constant in the second order region. In addition we find the rather surprising result that the phase transition persists up to very large values of $λ$, where the transition moves to (large) negative $β$.

hep-lat↗
arXiv1996

Order parameters and boundary effects in U(1) lattice gauge theory

We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an ``infinite'' current network, with an appropriate definition of ``infinite'' for the various types of boundary conditions imposed on the finite lattice. The probability for the occurrence of an ``infinite'' network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.

hep-lat↗
arXiv1995

Characterization of phases and boundary effects in U(1) gauge theory

We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining ``infinite'' on a finite lattice in a manner appropriate to the chosen boundary conditions. In addition for open and fixed boundary conditions we demonstrate the effects of inhomogeneities and provide examples of the reappearance of an energy gap.

hep-lat↗
arXiv1995

Phase transition and dynamical-parameter method in U(1) gauge theory

Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge theory in the neighborhood of the transition point are made difficult by the suppression of tunneling between the phases, which becomes very strong as soon as the volume of the lattice grows to any appreciable size. This problem can be avoided by making the monopole coupling a dynamical variable. In this manner one can circumvent the tunneling barrier by effectively riding on top of the peaks in the energy distribution which meet for sufficiently large monopole coupling. Here we present an efficient method for determining the parameters needed for this procedure, which can thus be implemented at low computational cost also on large lattices. This is particularly important for a reliable determination of the transition point. We demonstrate the working of our method on a 16^4 lattice. We obtain an equidistribution of configurations across the phase transition even for such a relatively large lattice size.

hep-lat↗