Phase transition and critical behaviour of the d=3 Gross-Neveu model

A second order phase transition for the three dimensional Gross-Neveu model is established for one fermion species N=1. This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent \nu = 0.63 and scalar and fermionic anomalous dimension \eta_\sigma = 0.31 and \eta_\psi = 0.11, respectively. We also compute critical exponents for other N. Our results are based on exact renormalization group equations.Comment: 4 pages, 1 figure; v4 corresponds to the published articl

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure

Photoproduction of meson and baryon resonances in a chiral unitary approach

By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. The meson baryon sector can also be tackled along similar lines. We report on an update of these results showing some examples of photon induced reactions where the techniques have been recently applied.Comment: Contribution to the Erice Summer School of Nuclear Physics, 21th course: Electromagnetic Probes and the Structure of Hadrons and Nuclei September 17th - 25th, 1999, Erice/Sicily/Ital

Thermodynamic perturbation theory for dipolar superparamagnets

Thermodynamic perturbation theory is employed to derive analytical expressions for the equilibrium linear susceptibility and specific heat of lattices of anisotropic classical spins weakly coupled by the dipole-dipole interaction. The calculation is carried out to the second order in the coupling constant over the temperature, while the single-spin anisotropy is treated exactly. The temperature range of applicability of the results is, for weak anisotropy (A/kT << 1), similar to that of ordinary high-temperature expansions, but for moderately and strongly anisotropic spins (A/kT > 1) it can extend down to the temperatures where the superparamagnetic blocking takes place (A/kT \sim 25), provided only the interaction strength is weak enough. Besides, taking exactly the anisotropy into account, the results describe as particular cases the effects of the interactions on isotropic (A = 0) as well as strongly anisotropic (A \to \infty) systems (discrete orientation model and plane rotators).Comment: 15 pages, 3 figure

A Systematic Study on Energy Dependence of Quasi-Periodic Oscillation Frequency in GRS 1915+105

Systematically studying all the RXTE/PCA observations for GRS 1915+105 before November 2010, we have discovered three additional patterns in the relation between Quasi-Periodic Oscillation (QPO) frequency and photon energy, extending earlier outcomes reported by Qu et al. (2010). We have confirmed that as QPO frequency increases, the relation evolves from the negative correlation to positive one. The newly discovered patterns provide new constraints on the QPO models

Helicity Amplitudes of the Lambda(1670) and two Lambda(1405) as dynamically generated resonances

We determine the helicity amplitudes A_1/2 and radiative decay widths in the transition Lambda(1670) to gamma Y (Y=Lambda or Sigma^0). The Lambda(1670) is treated as a dynamically generated resonance in meson-baryon chiral dynamics. We obtain the radiative decay widths of the Lambda(1670) to gamma Lambda as 3 \pm 2 keV and to gamma Sigma^0 as 120 \pm 50 keV. Also, the Q^2 dependence of the helicity amplitudes A_1/2 is calculated. We find that the K Xi component in the Lambda(1670) structure, mainly responsible for the dynamical generation of this resonance, is also responsible for the significant suppression of the decay ratio Gamma_{gamma Lambda}/Gamma_{gamma Sigma^0}. A measurement of the ratio would, thus, provide direct access to the nature of the Lambda(1670). To compare the result for the Lambda(1670), we calculate the helicity amplitudes A_1/2 for the two states of the Lambda(1405). Also, the analytic continuation of Feynman parameterized integrals of more complicated loop amplitudes to the complex plane is developed which allows for an internally consistent evaluation of A_1/2.Comment: 15 pages, 8 figure

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory