605 research outputs found
Non--perturbative tests of the fixed point action for SU(3) gauge theory
In this paper (the second of a series) we extend our calculation of a
classical fixed point action for lattice pure gauge theory to include
gauge configurations with large fluctuations. The action is parameterized in
terms of closed loops of link variables. We construct a few-parameter
approximation to the classical FP action which is valid for short correlation
lengths. We perform a scaling test of the action by computing the quantity where the string tension is measured from the
torelon mass . We measure on lattices of fixed physical
volume and varying lattice spacing (which we define through the
deconfinement temperature). While the Wilson action shows scaling violations of
about ten per cent, the approximate fixed point action scales within the
statistical errors for . Similar behaviour is found for
the potential measured in a fixed physical volume.Comment: 28 pages (latex) + 11 figures (Postscript), uuencode
Setting the scale for the Luescher-Weisz action
We study the quark-antiquark potential of quenched SU(3) lattice gauge theory
with the Luescher-Weisz action. After blocking the gauge fields with the
recently proposed hypercubic transformation we compute the Sommer parameter,
extract the lattice spacing a and set the scale at 6 different values of the
gauge coupling in a range from a = 0.084 fm to 0.136 fm.Comment: Remarks and references added, to appear in Phys. Rev.
Fixed-point action for fermions in QCD
We report our progress constructing a fixed-point action for fermions
interacting with SU(3) gauge fields.Comment: 3 pages, LaTeX file. Talk presented at LATTICE96(improvement
Anomalous fluctuations in phases with a broken continuous symmetry
It is shown that the Goldstone modes associated with a broken continuous
symmetry lead to anomalously large fluctuations of the zero field order
parameter at any temperature below T_c. In dimensions 2<d<4, the variance of
the extensive spontaneous magnetization scales as L^4 with the system size L,
independent of the order parameter dynamics. The anomalous scaling is a
consequence of the 1/q^{4-d} divergence of the longitudinal susceptibility. For
ground states in two dimensions with Goldstone modes vanishing linearly with
momentum, the dynamical susceptibility contains a singular contribution
(q^2-\omega^2/c^2)^{-1/2}. The dynamic structure factor thus exhibits a
critical continuum above the undamped spin wave pole, which may be detected by
neutron scattering in the N\'eel-phase of 2D quantum antiferromagnets.Comment: final version, minor change
A New Approach to Stochastic State selections in Quantum Spin Systems
We propose a new type of Monte Carlo approach in numerical studies of quantum
systems. Introducing a probability function which determines whether a state in
the vector space survives or not, we can evaluate expectation values of powers
of the Hamiltonian from a small portion of the full vector space. This method
is free from the negative sign problem because it is not based on importance
sampling techniques. In this paper we describe our method and, in order to
examine how effective it is, present numerical results on the 4x4, 6x6 and 8x8
Heisenberg spin one-half model. The results indicate that we can perform useful
evaluations with limited computer resources. An attempt to estimate the lowest
energy eigenvalue is also stated.Comment: 10 pages, 2 figures, 8 table
A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model
A scaling hypothesis for the n-particle spectral densities of the O(3)
nonlinear sigma-model is described. It states that for large particle numbers
the n-particle spectral densities are ``self-similar'' in being basically
rescaled copies of a universal shape function. This can be viewed as a
2-dimensional, but non-perturbative analogue of the KNO scaling in QCD.
Promoted to a working hypothesis, it allows one to compute the two point
functions at ``all'' energy or length scales. In addition, the values of two
non-perturbative constants (needed for a parameter-free matching of the
perturbative and the non-perturbative regime) are determined exactly.Comment: 9 Pages, Latex, 3 Postscript Figure
Improving lattice perturbation theory
Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at the `tadpole renormalized' coupling to be compared to the non-perturbative numerical value Comment: Plain TeX, 8 page
High density QCD with static quarks
We study lattice QCD in the limit that the quark mass and chemical potential
are simultaneously made large, resulting in a controllable density of quarks
which do not move. This is similar in spirit to the quenched approximation for
zero density QCD. In this approximation we find that the deconfinement
transition seen at zero density becomes a smooth crossover at any nonzero
density, and that at low enough temperature chiral symmetry remains broken at
all densities.Comment: LaTeX, 18 pages, uses epsf.sty, postscript figures include
Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution
In a system where chiral symmetry is spontaneously broken, the low energy
eigenmodes of the continuum Dirac operator are extended. On the lattice, due to
discretization effects, the Dirac operator can have localized eigenmodes that
affect physical quantities sensitive to chiral symmetry. While the infrared
eigenmodes of the Wilson Dirac operator are usually extended even on coarse
lattices, the chiral overlap operator has many localized eigenmodes in the
physical region, especially in mixed action simulations. Depending on their
density, these modes can introduce strong lattice artifacts. The effect can be
controlled by changing the parameters of the overlap operator, in particular
the clover improvement term and the center of the overlap projection.Comment: 16 pages, 6 figure
Finite-size scaling of the helicity modulus of the two-dimensional O(3) model
Using Monte Carlo methods, we compute the finite-size scaling function of the
helicity modulus of the two-dimensional O(3) model and compare it to
the low temperature expansion prediction. From this, we estimate the range of
validity for the leading terms of the low temperature expansion of the
finite-size scaling function and for the low temperature expansion of the
correlation length. Our results strongly suggest that a Kosterlitz-Thouless
transition at a temperature is extremely unlikely in this model.Comment: 4 pages, 3 Postscript figures, to appear in Phys. Rev. B Jan. 1997 as
a Brief Repor
- âŠ