The extended gaussian ensemble and metastabilities in the Blume-Capel model

The Blume-Capel model with infinite-range interactions presents analytical solutions in both canonical and microcanonical ensembles and therefore, its phase diagram is known in both ensembles. This model exhibits nonequivalent solutions and the microcanonical thermodynamical features present peculiar behaviors like nonconcave entropy, negative specific heat, and a jump in the thermodynamical temperature. Examples of nonequivalent ensembles are in general related to systems with long-range interactions that undergo canonical first-order phase transitions. Recently, the extended gaussian ensemble (EGE) solution was obtained for this model. The gaussian ensemble and its extended version can be considered as a regularization of the microcanonical ensemble. They are known to play the role of an interpolating ensemble between the microcanonical and the canonical ones. Here, we explicitly show how the microcanonical energy equilibrium states related to the metastable and unstable canonical solutions for the Blume-Capel model are recovered from EGE, which presents a concave "extended" entropy as a function of energy.Comment: 6 pages, 5 eps figures. Presented at the XI Latin American Workshop on Nonlinear Phenomena, October 05-09 (2009), B\'uzios (RJ), Brazil. To appear in JPC

Comparison among HB-inspired algorithms for continuous-spin systems and gauge fields

We propose a new local algorithm for the thermalization of n-vector spin models, which can also be used in the numerical simulation of SU(N) lattice gauge theories. The algorithm combines heat-bath (HB) and micro-canonical updates in a single step -- as opposed to the hybrid overrelaxation method, which alternates between the two kinds of update steps -- while preserving ergodicity. We test our proposed algorithm in the case of the one-dimensional 4-vector spin model and compare its performance with the standard HB algorithm and with other HB-inspired algorithms.Comment: 6 pages, 4 figures. Work presented at the IV Brazilian Meeting on Simulational Physics -- Ouro Preto - MG/Brazil, August 200

Methods for calculating nonconcave entropies

Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: i) microcanonical contraction, ii) metastable branches of the free energy, iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, iv) restricted canonical ensemble, and v) inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method.Comment: v1: 22 pages, IOP style, 7 color figures, contribution for the JSTAT special issue on Long-range interacting systems. v2: Open problem and references added, minor typos corrected, close to published versio

On unifying the description of meson and baryon properties

A Poincare' covariant Faddeev equation is presented, which enables the simultaneous prediction of meson and baryon observables using the leading-order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q^2-evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r_1^{nu}>r_1^{nd}. The proton electric-magnetic form factor ratio falls with increasing Q^2.Comment: 5 pages, 4 figures, 1 tabl

Delta-baryon mass in a covariant Faddeev approach

We present a calculation of the three-quark core contribution to the mass of the Delta-baryon in a Poincare-covariant Faddeev framework. A consistent setup for the dressed-quark propagator, the quark-quark and quark-diquark interactions is used, where all the ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in rainbow-ladder truncation. We discuss the evolution of the Delta mass with the current-quark mass and compare to the previously obtained mass of the nucleon.Comment: 8 pages, 2 figures, 1 tabl

Hadron Spectroscopy with Dynamical Chirally Improved Fermions

We simulate two dynamical, mass degenerate light quarks on 16^3x32 lattices with a spatial extent of 2.4 fm using the Chirally Improved Dirac operator. The simulation method, the implementation of the action and signals of equilibration are discussed in detail. Based on the eigenvalues of the Dirac operator we discuss some qualitative features of our approach. Results for ground state masses of pseudoscalar and vector mesons as well as for the nucleon and delta baryons are presented.Comment: 26 pages, 17 figures, 10 table

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

The gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic properties yielded by the extended gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range interactions are analyzed. This model presents different predictions for the first-order phase transition line according to the microcanonical and canonical ensembles. From the EGE approach, we explicitly work out the analytical microcanonical solution. Moreover, the general EGE solution allows one to illustrate in details how the stable microcanonical states are continuously recovered as the gaussian parameter $\gamma$ is increased. We found out that it is not necessary to take the theoretically expected limit $\gamma \to \infty$ to recover the microcanonical states in the region between the canonical and microcanonical tricritical points of the phase diagram. By analyzing the entropy as a function of the magnetization we realize the existence of unaccessible magnetic states as the energy is lowered, leading to a treaking of ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten, tricritical point calculations added. To appear in EPJ

Excitations of single-beauty hadrons

In this work we study the predominantly orbital and radial excitations of hadrons containing a single heavy quark. We present meson and baryon mass splittings and ratios of meson decay constants (e.g., $f_{B_s}/f_B$ and $f_{B_s'}/f_{B_s}$) resulting from quenched and dynamical two-flavor configurations. Light quarks are simulated using the chirally improved (CI) lattice Dirac operator at valence masses as light as $M_\pi \approx 350$ MeV. The heavy quark is approximated by a static propagator, appropriate for the $b$ quark on our lattices ($1/a \sim 1-2$ GeV). We also include some preliminary calculations of the $O(1/m_Q^{})$ kinetic corrections to the states, showing, in the process, a viable way of applying the variational method to three-point functions involving excited states. We compare our results with recent experimental findings.Comment: 23 pages, 18 figures, 17 tables; slight title change (Ed. killjoy); reference added; version to appear in Phys Rev

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure