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T. Neuhaus

Publications and source records attributed to T. Neuhaus.

At least 37 records · Page 2Linked to original sources
arXiv1997

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $ν\simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $ν\simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.

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arXiv1996

Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory

We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of $T1^{+-}$ gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents $δ$ and $β_{exp}$.

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arXiv1996

Critical Higgs Mass and Temperature Dependence of Gauge Boson Masses in the SU(2) Gauge-Higgs Model

We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from $60$ GeV up to $100$ GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. For Higgs-mass values larger than about $m_{H,c}=75.4(6)$ GeV the thermodynamic signature of the transition is described by a crossover. Close to this Higgs-mass value we investigate the vector boson propagator in Landau gauge. The calculated W-boson screening masses are compared with predictions based on gap equations.

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arXiv1996

Multicanonical Study of Continuum Physics in the D=2 $O(3)$ Nonlinear Sigma Model

Employing a variant of the Multicanonical Ensemble we study twisted spin configurations on periodic boxes in the $D=2$ $O(3)$ nonlinear sigma model for $β$-values inbetween $1.55$ to $3.1$. The free energy difference of twisted spin configurations is determined from the constraint effective potential. The finite size scaling behavior is in accordance with the asymptotically free nature of the continuum theory. Upon certain reasonable assumptions we determine the $Δβ( β)$-shift of the stiffness correlation length $ξ_s$. The mass-gap as determined by our analysis is ${m_0}=79.6(1.9)~Λ_{latt}$. This value agrees with the analytical result of the thermodynamic Bethe Ansatz ${m_0}=80.1~Λ_{latt}$.

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arXiv1996

Non-Gaussian fixed point candidates in the 4D compact U(1) gauge theories

Some interesting nonperturbative properties of the strongly coupled 4D compact U(1) lattice gauge theories, both without and with matter fields, are pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed point with $ν= 0.365(8)$ at the second order confinement-Coulomb phase transition. Thus a non-asymptotic free and nontrivial continuum limit of this theory, and of its various dual equivalents, in particular of a special case of the effective string theory, can be constructed. Including a scalar matter field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of the Higgs phase transition line. In the theory with both scalar and fermion matter fields, we demonstrate the existence of a tricritical point. Here, the chiral symmetry is broken, and the mass of unconfined composite fermions is generated dynamically. Appart from the Goldstone bosons, the spectrum contains also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling behavior is different from that in the NJL model and the nonperturbative renormalizability might thus be possible.

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arXiv1996

Four-dimensional pure compact U(1) gauge theory on a spherical lattice

We investigate the confinement-Coulomb phase transition in the four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The action contains the Wilson coupling beta and the double charge coupling gamma. The lattice is obtained from the 4D surface of the 5D cubic lattice by its radial projection onto a 4D sphere, and made homogeneous by means of appropriate weight factors for individual plaquette contributions to the action. On such lattices the two-state signal, impeding the studies of this theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a consistent finite-size scaling behavior of several bulk observables is found, with the correlation length exponent nu in the range nu = 0.35 - 40. These observables include Fisher zeros, specific-heat and cumulant extrema as well as pseudocritical values of beta at fixed gamma. The most reliable determination of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at gamma le 0 is thus very probably of 2nd order and belongs to the universality class of a non-Gaussian fixed point.

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arXiv1996

Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice

The line of phase transitions, separating the confinement and the Coulomb phases in the four-dimensional pure compact U(1) gauge theory with extended Wilson action, is reconsidered. We present new numerical evidence that a part of this line, including the original Wilson action, is of second order. By means of a high precision simulation on homogeneous lattices on a sphere we find that along this line the scaling behavior is determined by one fixed point with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the existence of a nontrivial and nonasymptotically free four-dimensional pure U(1) gauge theory in the continuum very probable. The universality and duality arguments suggest that this conclusion holds also for the monopole loop gas, for the noncompact abelian Higgs model at large negative squared bare mass, and for the corresponding effective string theory.

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arXiv1996

Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs Model

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar--gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find $m_w = 0.35(1)g^2T $ in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size $L^2\times L_z$ with $L=4-24$ and $L_z = 16 - 128$.

hep-lat↗
arXiv1995

Spin and Gauge Systems on Spherical Lattices

We present results for 2D and 4D systems on lattices with topology homotopic to the surface of a (hyper) sphere $S^2$ or $S^4$. Finite size scaling is studied in situations with phase transitions of first and second order type. The Ising and Potts models exhibit the expected behaviour; for the 4D pure gauge $U(1)$ theory we find consistent scaling indicative of a second order phase transition with critical exponent $ν\simeq 0.36(1)$.

hep-lat↗
arXiv1994

Evidence for a Critical Behavior in $4D$ Pure Compact QED

We present evidence about a critical behavior of $4D$ compact QED (CQED) pure gauge theory. Regularizing the theory on lattices homotopic to a sphere, we present evidence for a critical, i.e. second order like behavior at the deconfinement phase transition for certain values of the coupling parameter $γ$.

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arXiv1994

Compact lattice QED with Wilson fermions

We study the phase structure and the chiral limit of $4d$ compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson gauge action and also a modified one suppressing lattice artifacts. Different techniques and observables to locate the chiral limit are discussed.

hep-lat↗
arXiv1994

Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

We study the pure gauge model on a lattice manifold with trivial fundamental homotopy group, homotopically equivalent to an $S_4$. Monopole loops may fluctuate freely on that lattice without restrictions due to the boundary conditions. For the original Wilson action on the hypertorus there is an established two-state signal in energy distribution functions which disappears for the new geometry. Our finite size scaling analysis suggests stringent upper bounds on possible discontinuities in the plaquette action. However, no consistent asymptotic finite size scaling behaviour is observed.

hep-lat↗
arXiv1994

Effective Scalar Field Theory for the Electroweak Phase Transition

We investigate an effective model for the finite temperature restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the $3+1$ dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a $3$-dimensional $O(4)$ ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, $m_H=37~{\rm GeV}$, considered in the present investigation, we find a discontinuous symmetry restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first order phase transition as compared to the mean field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first order transition could result only from non-perturbative effects related to the gauge degrees of freedom.

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arXiv1994

Multicanonical study of $D=2$ $O(3)$ nonlinear $σ$-model

We present a new and exploratory approach to determine the $Δβ(β)$-shift in the $O(3)$ nonlinear $σ$-model. The method is based on a scaling hypothesis for a free energy difference, which is assumed to be valid in a situation where the mass gap correlation length $ξ$ is of the order or larger than the linear extent $L$ of the considered square lattice sizes. The free energy difference arises from the finite volume constraint effective potential of the theory. While the constraint effective potential is calculated in numerical simulations employing a variant of the multicanonical ensemble on medium sized lattices, it is possible to estimate $Δβ(β)$ up to a value of $β=2.8$ in the standard parameterization of the model.

hep-lat↗
arXiv1993

The analysis of Polyakov loop and spin correlators in finite volumes

We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye screening mass $~μ_D/T\approx4~$, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.

hep-lat↗
arXiv1993

The First Order Signal in Pure U(1) Gauge Theory May be Fake

We study the deconfinement phase transition of compact $U(1)$ pure lattice gauge theory with the Wilson action on {\em closed topology} lattices. In contrast to studies of compact QED on {\em hypercubic lattices with periodic boundary conditions}, we find no metastability signal at the phase transition on the lattices with the topology of a sphere. Thus the determination of the order of this phase transition has to be reconsidered. We argue that different properties of closed monopole loops on these topological inequivalent lattices might be responsible for the effect.

hep-lat↗
arXiv1993

A Determination of Interface Free Energies

We determine the interface free energy $F_{o.d.}$ between disordered and ordered phases in the q=10 and q=20 2-d Potts models using the results of multicanonical Monte Carlo simulations on $L^2$ lattices, and suitable finite volume estimators. Our results, when extrapolated to the infinite volume limit, agree to high precision with recent analytical calculations. At the transition point $β_t$ the probability distribution function of the energy exhibits two maxima. Their locations have $1/L^2$ corrections, in contradiction with claims of $1/L$ behavior made in the literature. Our data show a flat region inbetween the two maxima which characterizes two domain configurations.

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