Asymptotically free theories based on discrete subgroups

We study the critical behavior of discrete spin models related to the 2d O(3) non-linear sigma model. Precise numerical results suggest that models with sufficiently large discrete subgroups are in the same universality class as the original sigma model. We observe that at least up to correlation lengths $\xi\approx 300$ the cut-off effects follow effectively an $\propto a$ behaviour both in the O(3) and in the dodecahedron model.Comment: 4 pages, 3 figures, Lattice 2000 (Spin Models

The SU(3) deconfining phase transition with Symanzik action

We report on the determination of the deconfining temperature in SU(3) pure gauge theory, using the Symanzik tree level improved action, on lattices of size 3 x 12^3, 4 x 16^3, 5 x 20^3, 6 x24^3. We find that the asymptotic scaling violation pattern is similar to the one observed using the Wilson action. We conclude that the irrelevant operators do not affect, in the range of couplings considered, the lattice beta function. An analysis based on an effective coupling formulation shows an apparent improvement.Comment: 8 pages, report IFUP-TH 12/9

Gauge invariant extremization on the lattice

Recently, a method was proposed and tested to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize \int(\dl S/\dl A_\mu)^2. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we show how extremization can be formulated in a way that preserves gauge invariance on the lattice. The method applies to any gauge group and any lattice action. The procedure is worked out in detail for the standard plaquette action with gauge groups U(1) and SU(N).Comment: 7 pages, LaTeX, Oxford preprint OUTP-92-16

Verification of O(a) improvement

The status of simulations using the non-perturbatively O(a) improved Wilson action in the quenched approximation is reviewed. The impact of non-perturbative improvement on the hadronic mass spectrum and the size of residual lattice artefacts in spectral quantities and decay constants are assessed.Comment: Plenary talk presented at LATTICE '97, 6 pages, LaTeX, espcrc2.sty, 6 postscript files, to be included with eps

Classical improvement of lattice actions and quantum effects: a unified view

The possibility of removing the one-loop perturbative effects of lattice artifacts by a proper choice of the lattice action is explored, and found to depend crucially on the properties of the physical quantity considered. In this respect the finite-space-volume mass gap m(L) is an improved observable. We find an explicit momentum space representation of the one-loop contribution to m(L) for arbitrary lattice actions in the case of two-dimensional O(N) sigma models. We define a ``tree perfect'' Symanzik action and find that it formally removes all one-loop lattice artifacts in m(L). On-shell improved actions do not share this property.Comment: 10 pages, revte

Improved actions of the staggered fermion

We have studied $O(a^2)$ improved lattice QCD with the staggered fermion by using Symanzik's program. We find that there are 5 dimension-6 fermion bilinears and gauge operators. In addition, there are 10 four-fermion operators which are absent at the tree-level and tadpole-improved tree-level.Comment: 3 pages, Latex, talk presented at LATTICE''97(Improvement

Unexpected results in asymptotically free quantum field theories

We study the behavior of asymptotically free (AF) spin and gauge models when their continuous symmetry group is replaced by different discrete non-Abelian subgroups. Precise numerical results with relative errors down to O(0.1%) suggest that the models with large subgroups are in the universality class of the underlying original models. We argue that such a scenario is consistent with the known properties of AF theories. The small statistical errors allow a detailed investigation of the cut-off effects also. At least up to correlation lengths ~300 they follow effectively an O(a) rather than the expected O(a^2) form both in the O(3) and in the dodecahedron model.Comment: 16 pages, 7 figures, some omissions corrected, a reference adde

Predicting the Aoki Phase using the Chiral Lagrangian

This work is concerned with the phase diagram of Wilson fermions in the mass and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian, supplemented by additional terms proportional to powers of the lattice spacing. We find two possible phase structures at non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken flavor and parity, with two massless Goldstone-pions, and a width $\Delta m_0 \sim a^3$; (2) There is no spontaneous symmetry breaking, and all three pions have equal mass of order $a$. Present numerical simulations suggest that the former option is realized.Comment: LATTICE98(spectrum), 3 pages, 2 figures, LaTex, uses espcrc2.st

Determining Lines of Constant Physics in the Confinement Phase of the SU(2) Higgs Model

We present a method for finding lines of constant physics in the confinement phase of the SU(2) Higgs model on the lattice. The model is considered at finite values of the cut-off where it behaves like an effective field theory with three independent couplings. In particular, a renormalised quantity sensitive to a variation of the bare Higgs quartic self-coupling is constructed from generalised Binder cumulants. Numerical results for the non-perturbative matching of the bare parameters of the model between beta=2.2 and beta=2.4 are presented.Comment: 10 pages, 4 figures, small changes in the introductio

Non-perturbative O(a) improvement of the vector current

We discuss non-perturbative improvement of the vector current, using the Schroedinger Functional formalism. By considering a suitable Ward identity, we compute the improvement coefficient which gives the O(a) mixing of the tensor current with the vector one.Comment: 3 pages (LaTeX, 2 ps figures, styles), talk presented at Lattice 9