Spontaneous Breaking of Flavor Symmetry and Parity in the Nambu-Jona-Lasinio Model with Wilson Fermions

We study the lattice \njl~model with two flavors of Wilson fermions in the large $N$ limit, where $N$ is the number of `colors'. For large values of the four-fermion coupling we find a phase in which both, flavor symmetry and parity, are spontaneously broken. In accordance with general expectations there are three massless pions on the phase boundary, but only two of them remain massless inside the broken phase. This is analogous to earlier results obtained in lattice QCD, indicating that this behavior is a very general feature of the Wilson term.Comment: 7 pages, 4 figures, LATEX, tared and uuencode

Finite-Temperature Phase Structure of Lattice QCD with the Wilson Quark Action for Two and Four Flavors

We present further analyses of the finite-temperature phase structure of lattice QCD with the Wilson quark action based on spontaneous breakdown of parity-flavor symmetry. Results are reported on (i) an explicit demonstration of spontaneous breakdown of parity-flavor symmetry beyond the critical line, (ii) phase structure and order of chiral transition for the case of $N_f=4$ flavors, and (iii) approach toward the continuum limit.Comment: Poster presented at LATTICE96(finite temperature); 4 pages, Latex, uses espcrc2 and epsf, seven ps figures include

Chiral perturbation theory with Wilson-type fermions including a2a^2 effects: Nf=2N_f=2 degenerate case

We have derived the quark mass dependence of $m_{\pi}^2$, $m_{\rm AWI}$ and $f_{\pi}$, using the chiral perturbation theory which includes the $a^2$ effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the $N_f=2$ degenerate quarks. Distinct features of the results are (1) the additive renormalization for the mass parameter $m_q$ in the Lagrangian, (2) $O(a)$ corrections to the chiral log ($m_q\log m_q$) term, (3) the existence of more singular term, $\log m_q$, generated by $a^2$ contributions, and (4) the existence of both $m_q\log m_q$ and $\log m_q$ terms in the quark mass from the axial Ward-Takahashi identity, $m_{\rm AWI}$. By fitting the mass dependence of $m_\pi^2$ and $m_{\rm AWI}$, obtained by the CP-PACS collaboration for $N_f=2$ full QCD simulations, we have found that the data are consistently described by the derived formulae. Resumming the most singular terms $\log m_q$, we have also derived the modified formulae, which show a better control over the next-to-leading order correction.Comment: 21 pages, 4 figures (10 eps files), Revtex4, some discussions and references added, the final version to appear in PR

Two-dimensional Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Density

We analytically investigate the 2-dimensional Gross-Neveu model at finite temperature and density using Wilson fermion action. The relation between the phase structure on the lattice and that in the continuum is clarified.Comment: LATTICE98(hightemp), 3 pages, 3 eps figure

Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere

In the previous papers, we studied the 't Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that the configuration space can be classified into the topological sectors. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and consider the index theorem in these cases.Comment: Latex2e, 37 pages, 3 figure

Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential

We investigate the phase structure of the two-dimensional lattice Gross-Neveu model formulated with the Wilson fermion action to leading order of 1/N expansion. Structural change of the parity-broken phase under the influence of finite temperature and chemical potential is studied. The connection between the lattice phase structure and the chiral phase transition of the continuum theory is clarified.Comment: 42 pages, 20 EPS figures, using REVTe

Passing through the `chiral limit' in quenched QCD with Wilson fermions

We investigate the limit of vanishing quark mass in quenched lattice QCD with unimproved Wilson fermions at $\beta=6.0$. Exploiting the correlations of propagators at different time slices we extract pion masses extremely close to the `chiral limit', despite the presence of `exceptional configurations'. With this at hand, the existence of quenched chiral logarithms can be demonstrated, provided, finite size effects are small. With reference to the phase diagram proposed by Aoki also the range $\kappa > \kappa_c$ is investigated. The width of a potential parity-flavor violating phase can, if at all, hardly be resolved.Comment: LATTICE98(spectrum