On Witten's global anomaly for higher SU(2) representations

The spectral flow of the overlap operator is computed numerically along a particular path in gauge field space. The path connects two gauge equivalent configurations which differ by a gauge transformation in the non-trivial class of pi_4(SU(2)). The computation is done with the SU(2) gauge field in the fundamental, the 3/2, and the 5/2 representation. The number of eigenvalue pairs that change places along this path is established for these three representations and an even-odd pattern predicted by Witten is verified.Comment: 24 pages, 12 eps figure

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking scheme and added comments to discussio

Chiral perturbation theory at O(a^2) for lattice QCD

We construct the chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through order $a^2$. The chiral Lagrangian is then derived, including terms of order $a^2$, which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$, and appear in the Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking terms enter the Symanzik action at order $a^2$, but contribute to the chiral Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no order $a^2$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.Comment: 25 pages, LaTeX2e; references adde

Long Range Dynamics Related to Magnetic Impurity in the 2D Heisenberg Antiferromagnet

We consider a magnetic impurity in the two-dimensional Heisenberg antifferomagnet with long range antiferromagnetic order. At low temperature the impurity magnetic susceptibility has a Curie term ($\propto 1/T$) and a logarithmic correction ($\propto \ln(T)$). We calculate the correction and derive related Ward identity for the impurity-spin-wave vertex.Comment: 5 pages, 6 figure

Schwinger-boson approach to quantum spin systems: Gaussian fluctuactions in the "natural" gauge

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1-J2 antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for 0.53 < J2/J1 < 0.64. This result is obtained by considering the corrections to the spin stiffness on large lattices and extrapolating to the thermodynamic limit, which avoids the infinite-lattice infrared divergencies associated to Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.Comment: 4 pages, Latex, 3 figures included as eps files,minor correction

Atributos de cor em filés de peixes capturados no reservatório da Usina Hidrelétrica do Lageado, estado do Tocantins.

Objetivando caracterizar colorimetricamente os filés de quatro espécies de peixe capturadas no reservatório da Usina Hidrelétrica do Lageado, estado do Tocantins, foram selecionadas, ao todo, 47 amostras de peixes identificados como mandi-moela (Pimelodina flavipinnis), cuiú-cuiú (Oxydoras niger), mapará (Hypophthalmus edentatus) e corvina (Plagioscion squamosissimus).Organizado por: Sílvio Ricardo Maurano; AQUACIÊNCIA 2012

Spectral Properties of the Overlap Dirac Operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE

On the presence of mid-gap states in CaV4O9

Using exact diagonalizations of finite clusters with up to 32 sites, we study the $J_1-J_2$ model on the 1/5 depleted square lattice. Spin-spin correlation functions are consistent with plaquette order in the spin gap phase which exists for intermediate values of $J_2/J_1$. Besides, we show that singlet states will be present in the singlet-triplet gap if $J_2/J_1$ is not too small ($J_2/J_1 \gtrsim 0.47$). We argue that this property should play a central role in determining the exchange integrals in ${\rm CaV}_4{\rm O}_9$Comment: 4 pages, 5 postscript figure

Rectangular Wilson Loops at Large N

This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.Comment: 47 pages, 21 figures, 8 table

Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR