The correlation length of the Heisenberg antiferromagnet with arbitrary spin S

Experiments and numerical data on the correlation length for large S disagree strongly with the theoretical prediction based on the effective field theory prescription of the magnon physics. The reason is that for large S, at any accessible correlation lengths, the cut-off effects from the non-magnon scales become large and can not be treated by an effective field theory. We study these effects in a spin-wave expansion. The corrected prediction connects the renormalized classical and the classical scaling regions smoothly and comes close to the data.Comment: 10 pages, 1 figur

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 $SU(3)$ 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 $G = L \sqrt{\sigma(L)}$ where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L \sigma(L)$. We measure $G$ on lattices of fixed physical volume and varying lattice spacing $a$ (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 $1/2 \ge aT_c \ge 1/6$. Similar behaviour is found for the potential measured in a fixed physical volume.Comment: 28 pages (latex) + 11 figures (Postscript), uuencode

The QCD rotator in the chiral limit

The low lying spectrum of QCD in the delta-regime is calculated here in chiral perturbation theory up to NNL order. The spectrum has a simple form in terms of the pion decay constant F and a combination of the low energy constants Lambda1 and Lambda2. Since measuring low lying stable masses is among the easiest numerical tasks, the results should help fixing these parameters to good precision.Comment: 17 pages; typos are corrected and a paragraph added for better understanding; the present version is identical with the published paper in N.Phys.B. except a typo in eq(35) which is also corrected her

First results from a parametrized Fixed-Point QCD action

We have constructed a new fermion action which is an approximation to the (chirally symmetric) Fixed-Point action, containing the full Clifford algebra with couplings inside a hypercube and paths built from renormalization group inspired fat links. We present an exploratory study of the light hadron spectrum and the energy-momentum dispersion relation.Comment: Lattice2001(improvement), 3 pages, based on a talk by S.H; reference update

Perfect topological charge for asymptotically free theories

The classical equations of motion of the perfect lattice action in asymptotically free $d=2$ spin and $d=4$ 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 $d=2$ O(3) non--linear $\sigma$--model and the topological susceptibility is measured to high precision in the range of correlation lengths $\xi \in (2 - 60)$. 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

Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents

In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Sigma and the topological susceptibility chi_t, and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions.Comment: Lattice2001(chiral), based on a talk by T.J. and a poster by K.H., 6 page

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.

Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.Comment: 14 pages, 3 figures, late

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

Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change