865 research outputs found
Perfect topological charge for asymptotically free theories
The classical equations of motion of the perfect lattice action in
asymptotically free spin and gauge models possess scale invariant
instanton solutions. This property allows the definition of a topological
charge on the lattice which is perfect in the sense that no topological defects
exist. The basic construction is illustrated in the O(3) non--linear
--model and the topological susceptibility is measured to high
precision in the range of correlation lengths . Our results
strongly suggest that the topological susceptibility is not a physical quantity
in this model.Comment: Contribution to Lattice'94, 3 pages PostScript, uuencoded compresse
Four-loop free energy for the 2D O(n) nonlinear sigma-model with 0-loop and 1-loop Symanzik improved actions
We calculate up to four loops the free energy of the two-dimensional (2D)
O(n) nonlinear sigma-model regularized on the lattice with the 0-loop and
1-loop Symanzik improved actions. An effective coupling constant based on this
calculation is defined.Comment: 26 pages, Revtex. More details about the calculation procedur
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.
Towards Weyl fermions on the lattice without artefacts
In spite of the breakthrough in non-perturbative chiral gauge theories during
the last decade, the present formulation has stubborn artefacts. Independently
of the fermion representation one is confronted with unwanted CP violation and
infinitely many undetermined weight factors. Renormalization group identifies
the culprit. We demonstrate the procedure on Weyl fermions in a real
representation
Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials
We show how to compute real space renormalization group flows in lattice
field theory by a self-consistent method. In each step, the integration over
the fluctuation field (high frequency components of the field) is performed by
a saddle point method. The saddle point depends on the block-spin. Higher
powers of derivatives of the field are neglected in the actions, but no
polynomial approximation in the field is made. The flow preserves a simple
parameterization of the action. In this paper we treat scalar field theories as
an example.Comment: 52 pages, uses pstricks macro, three ps-figure
1-Loop improved lattice action for the nonlinear sigma-model
In this paper we show the Wilson effective action for the 2-dimensional
O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop
approximation for the nonlinear choice of blockspin , \Phi(x)=
\Cav\phi(x)/{|\Cav\phi(x)|},where \Cav is averaging of the fundamental field
over a square of side .
The result for is composed of the classical perfect action with a
renormalized coupling constant , an augmented contribution from a
Jacobian, and further genuine 1-loop correction terms. Our result extends
Polyakov's calculation which had furnished those contributions to the effective
action which are of order , where is the lattice spacing
of the fundamental lattice. An analytic approximation for the background field
which enters the classical perfect action will be presented elsewhere.Comment: 3 (2-column format) pages, 1 tex file heplat99.tex, 1 macro package
Espcrc2.sty To appear in Nucl. Phys. B, Proceedings Supplements Lattice 9
Spectrum of the fixed point Dirac operator in the Schwinger model
Recently, properties of the fixed point action for fermion theories have been
pointed out indicating realization of chiral symmetry on the lattice. We check
these properties by numerical analysis of the spectrum of a parametrized fixed
point Dirac operator investigating also microscopic fluctuations and fermion
condensation.Comment: LATTICE98(improvement), 3 pages, 3 figure
The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
The correlation length of the square-lattice spin-1/2 Heisenberg
antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime.
Our novel approach combines a very efficient loop cluster algorithm --
operating directly in the Euclidean time continuum -- with finite-size scaling.
This enables us to probe correlation lengths up to
lattice spacings -- more than three orders of magnitude larger than any
previous study. We resolve a conundrum concerning the applicability of
asymptotic-scaling formulae to experimentally- and numerically-determined
correlation lengths, and arrive at a very precise determination of the
low-energy observables. Our results have direct implications for the
zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor
modifications for final submission to Physical Review Letters. (accepted by
PRL
Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model
Polyakov's calculation of the effective action for the 2d nonlinear
sigma-Model is generalized by purely analytic means to include contributions
which are not UV-divergent and which depend on the choice of block spin. An
analytic approximation to the background field which determines the classical
perfect action is given, and approximations to the 1-loop correction are found.
The results should be useful for numerical simulations.Comment: 38 p, 1 figur
Four loop results for the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik actions
We present complete three loop results and preliminary four loop results for
the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik improved
actions. This calculation aims to test the improvement in the numerical
precision that the combination of Symanzik actions and effective couplings can
give in Monte Carlo simulations.Comment: LATTICE99(spin models). 3 pages, contains espcrc2.sty fil
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