The spectrum of massive excitations of 3d 3-state Potts model and universality

We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken phase (a) near the second order Ising critical point in the temperature - magnetic field plane and (b) near the weakly first order transition point at zero magnetic field. In the case (a), we compare the mass spectrum with the prediction from universality of mass ratios in the 3$d$ Ising class; in the case (b), we determine a mass ratio to be compared with the corresponding one in the spectrum of screening masses of the (3+1)$d$ SU(3) pure gauge theory at finite temperature in the deconfined phase near the transition. The agreement in the comparison in the case (a) would represent a non-trivial test of validity of the conjecture of spectrum universality. A positive answer to the comparison in the case (b) would suggest the possibility to extend this conjecture to weakly first order phase transitions.Comment: 20 pages, 12 figures; uses axodraw.st

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

Factors Regulating the Discharge Frequency in Optomotor Fibres Of Carcinus Maenas

The influence of the excited state of the animal on various motor neurone discharges and accompanying muscle action potentials was studied in the eyestalk of the crab, Carcinus maenas. In most cases large increases in firing frequency could be obtained during such states. An exception is the tonic eye-withdrawal system in which an inhibitory effect is caused. A pronounced difference in habituation to constant stimuli between spring and summer was found for the position fibres; in spring it was slow and in summer much quicker

Finite-size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.Comment: 6 pages. Several comments and one reference added, results unchange

One-loop Reggeon-Reggeon-gluon vertex at arbitrary space-time dimension

In order to check the compatibility of the gluon Reggeization in QCD with the $s$-channel unitarity, the one-loop correction to the Reggeon-Reggeon-gluon vertex must be known at arbitrary space-time dimension $D$. We obtain this correction from the gluon production amplitude in the multi-Regge kinematics and present an explicit expression for it in terms of a few integrals over the transverse momenta of virtual particles. The one-gluon contribution to the non-forward BFKL kernel at arbitrary $D$ is also obtained.Comment: 22 pages, LaTe

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

Efficient simulated tempering with approximated weights: Applications to first-order phase transitions

Simulated tempering (ST) has attracted a great deal of attention in the last years, due to its capability to allow systems with complex dynamics to escape from regions separated by large entropic barriers. However its performance is strongly dependent on basic ingredients, such as the choice of the set of temperatures and their associated weights. Since the weight evaluations are not trivial tasks, an alternative approximated approach was proposed by Park and Pande (Phys. Rev. E {\bf 76}, 016703 (2007)) to circumvent this difficulty. Here we present a detailed study about this procedure by comparing its performance with exact (free-energy) weights and other methods, its dependence on the total replica number $R$ and on the temperature set. The ideas above are analyzed in four distinct lattice models presenting strong first-order phase transitions, hence constituting ideal examples in which the performance of algorithm is fundamental. In all cases, our results reveal that approximated weights work properly in the regime of larger $R$'s. On the other hand, for sufficiently small $R$ its performance is reduced and the systems do not cross properly the free-energy barriers. Finally, for estimating reliable temperature sets, we consider a simple protocol proposed at Comp. Phys. Comm. {\bf 128}, 2046 (2014).Comment: Published online in Comp. Phys. Comm. (2015

Realization of Uq(so(N))U_q(so(N)) within the differntial algebra on RqN{\bf R}_q^N

We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$. The algebra $Fun({\bf R}_q^N)$ of functions on ${\bf R}_q^N$ splits into a direct sum of irreducible vector representations of $U_{q^{-1}}(so(N))$; the latter are explicitly constructed as highest weight representations.Comment: 26 pages, 1 figur

Screening masses in the SU(3) pure gauge theory and universality

We determine from Polyakov loop correlators the screening masses in the deconfined phase of the (3+1)d SU(3) pure gauge theory at finite temperature near the transition, for two different channels of angular momentum and parity. Their ratio is compared with that of the massive excitations with the same quantum numbers in the 3d 3-state Potts model in the broken phase near the transition point at zero magnetic field. Moreover we study the inverse decay length of the correlation between the real parts and between the imaginary parts of the Polyakov loop and compare the results with expectations from perturbation theory and mean-field Polyakov loop models.Comment: 19 pages, 9 figures; version to appear on Nuclear Physics B (Section 3.1 revisited; a few comments, a table and a reference added; fit results included in Fig. 8

Triggering Active Galactic Nuclei in Hierarchical Galaxy Formation: Disk instability vs. Interactions

Using a semi analytic model for galaxy formation we investigate the effects of Black Hole accretion triggered by disk instabilities (DI) in isolated galaxies on the evolution of AGN. Specifically, we took on, developed and expanded the Hopkins & Quataert (2011) model for the mass inflow following disk perturbations, and compare the corresponding evolution of the AGN population with that arising in a scenario where galaxy interactions trigger AGN (IT mode). We extended and developed the DI model by including different disk surface density profiles, to study the maximal contribution of DI to the evolution of the AGN population. We obtained the following results: i) for luminosities corresponding to $M_{1450}\gtrsim -26$ the DI mode can provide the BH accretion needed to match the observed AGN luminosity functions up to $z \approx 4.5$; in such a luminosity range and redshift, it can compete with the IT scenario as the main driver of cosmological evolution of AGN; ii) The DI scenario cannot provide the observed abundance of high-luminosity QSO with $M_{1450}\lesssim -26$ AGN, as well as the abundance of high-redhshift $z \approx 4.5$ QSOs with $M_{1450}\lesssim -24$, while the IT scenario provides an acceptable match up to $z \approx 6$, as found in our earliest works; iii) The dispersion of the distributions of Eddington ratio for low- and intermediate-luminosity AGN (bolometric $L_{AGN}$ = $10^{43}$ - $10^{45}$ erg/s) is predicted to be much smaller in the DI scenario compared to the IT mode; iv) The above conclusions are robust with respect to the explored variants of the Hopkins & Quataert (2011) model. We discuss the physical origin of our findings, and how it is possible to pin down the dominant fueling mechanism in the low-intermediate luminosity range $M_{1450}\gtrsim -26$ where both the DI and the IT modes are viable candidates as drivers for the AGN evolution.Comment: Accepted for publication in Astronomy & Astrophysics, 24 pages, 8 figures; updated reference