On the spectral density of the Wilson operator

We summarize our recent determination [1] of the spectral density of the Wilson operator in the p-regime of Wilson chiral perturbation theory. We discuss the range of validity of our formula and a possible extension to our computation in order to better understand the behaviour of the spectral density in a finite volume close to the threshold.Comment: 7 pages, 2 figures, Proceedings for the XXIX International Symposium on Lattice Field Theor

Corrections to the Banks-Casher relation with Wilson quarks

The Banks-Casher relation links the spectral density of the Dirac operator with the existence of a chiral condensate and spontaneous breaking of chiral symmetry. This relation receives corrections from a finite value of the quark mass, a finite space-time volume and, if evaluated on a discrete lattice, from the finite value of the lattice spacing a. We present a status report of a determination of these corrections for Wilson quarks.Comment: 6 pages, 4 figures, Chiral Dynamics 2012 proceedin

Thermal operators and cluster topology in q-state Potts Model

We discuss a new class of identities between correlation functions which arise from a local Z_2 invariance of the partition function of the q-state Potts model on general graphs or lattices. Their common feature is to relate the thermal operators of the Potts model to some topological properties of the Fortuin-Kasteleyn clusters. In particular it turns out that any even correlation function can be expressed in terms of observables which probe the linking properties of these clusters. This generalises a class of analogous relations recently found in the Ising model.Comment: 6 pages, latex, enlarged version, accepted for publication in Journal of Physics

The epsilon regime with twisted mass Wilson fermions

We investigate the leading lattice spacing effects in mesonic two-point correlators computed with twisted mass Wilson fermions in the epsilon-regime. By generalizing the procedure already introduced for the untwisted Wilson chiral effective theory, we extend the continuum chiral epsilon expansion to twisted mass WChPT. We define different regimes, depending on the relative power counting for the quark masses and the lattice spacing. We explicitly compute, for arbitrary twist angle, the leading O(a^2) corrections appearing at NLO in the so-called GSM^* regime. As in untwisted WChPT, we find that in this situation the impact of explicit chiral symmetry breaking due to lattice artefacts is strongly suppressed. Of particular interest is the case of maximal twist, which corresponds to the setup usually adopted in lattice simulations with twisted mass Wilson fermions. The formulae we obtain can be matched to lattice data to extract physical low energy couplings, and to estimate systematic uncertainties coming from discretization errors.Comment: 26 pages, 3 figure

Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V=(1.8 fm)^4.Comment: 10 pages, 9 figures, v2: minor clarifications, version accepted by PR

Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the relative power counting $m\sim a \Lambda_{\rm QCD}^2$: in this situation discretisation effects can be treated as perturbation of the continuum behaviour. While this framework fails to describe lattice spectral density close to the threshold, it allows nevertheless to investigate important properties of the spectrum of the Wilson Dirac operator. We discuss the range of validity of our results and the possible implications in understanding the phase diagram of Wilson fermions.Comment: 27 pages, 4 figures; few typos corrected, added footnote, published versio

Mixed action computations on fine dynamical lattices

We report on our first experiences in simulating Neuberger valence fermions on CLS $N_f=2$ configurations with light sea quark masses and small lattice spacings. Valence quark masses are considered that allow to explore the matching to (partially quenched) chiral perturbation theory both in the $\epsilon$- and $p$-regimes. The setup is discussed, and first results are presented for spectral observables.Comment: 7 pages. Presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

Lattice Gauge Actions for Fixed Topology

We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the epsilon-regime and it is expected to help in numerical simulations with dynamical quarks.Comment: 3 pages. Talk presented at Quark Confinement and the Hadron Spectrum VI, Villasimius, Sardinia, Italy, September 21-25, 2004. References adde