The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity η=2mKN\eta = \frac{2m K}{N} for odd N

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta = \frac{2m K}{N}$ with odd $N$ where Q_{72} does not exist. We use this new Q-operator to study the functional relations in the Fabricius-McCoy comparison between the root-of-unity eight-vertex model and the superintegrable N-state chiral Potts model. By the compatibility of the constructed Q-operator with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we verify the set of functional relations of the root-of-unity eight-vertex model using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation, References added and updated-Journal versio

Injunction Against Prosecution of Divorce Actions in Other States

Aims: The formation scenario of extended counter-rotating stellar disks in galaxies is still debated. In this paper, we study the S0 galaxy IC 719 known to host two large-scale counter-rotating stellar disks in order to investigate their formation mechanism. Methods: We exploit the large field of view and wavelength coverage of the Multi Unit Spectroscopic Explorer (MUSE) spectrograph to derive two-dimensional (2D) maps of the various properties of the counter-rotating stellar disks, such as age, metallicity, kinematics, spatial distribution, the kinematical and chemical properties of the ionized gas, and the dust map. Results: Due to the large wavelength range, and in particular to the presence of the Calcium Triplet \u3bb\u3bb8498, 8542, 8662 \uc5 (CaT hereafter), the spectroscopic analysis allows us to separate the two stellar components in great detail. This permits precise measurement of both the velocity and velocity dispersion of the two components as well as their spatial distribution. We derived a 2D map of the age and metallicity of the two stellar components, as well as the star formation rate and gas-phase metallicity from the ionized gas emission maps. Conclusions: The main stellar disk of the galaxy is kinematically hotter, older, thicker and with larger scale-length than the secondary disk. There is no doubt that the latter is strongly linked to the ionized gas component: they have the same kinematics and similar vertical and radial spatial distribution. This result is in favor of a gas accretion scenario over a binary merger scenario to explain the origin of counter-rotation in IC 719. One source of gas that may have contributed to the accretion process is the cloud that surrounds IC 719

The TQ equation of the 8 vertex model for complex elliptic roots of unity

We extend our studies of the TQ equation introduced by Baxter in his 1972 solution of the 8 vertex model with parameter $\eta$ given by $2L\eta=2m_1K+im_2K'$ from $m_2=0$ to the more general case of complex $\eta.$ We find that there are several different cases depending on the parity of $m_1$ and $m_2$.Comment: 30 pages, LATE

An elliptic current operator for the 8 vertex model

We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to the concept of an elliptic current operator. We find that in sharp contrast with the corresponding formalism in the six-vertex model at roots of unity the current operator is not nilpotent with the consequence that in the construction of degenerate eigenstates of the transfer matrix an arbitrary number of exact strings can be added to the set of regular Bethe roots. Thus the original set of free parameters {s,t} of an eigenvector of T is enlarged to become {s,t,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers \lambda_{c,j} and arbitrary n.Comment: 16 pages, Latex typographic errors corrected, text added, reference added, accepted by Journal of Physics A,Mathematical and Genera

Temperature dependent spatial oscillations in the correlations of the XXZ spin chain

We study the correlation $$ for the XXZ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.Comment: 4 pages, REVTEX, 6 table

Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent $\theta$ of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent $\theta$ exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent $z$ shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.Comment: 10 figures, 4 tables and 14 page

Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension $d_H$ =1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. The topological effects become evident from the emergence of a logarithmic periodic oscillation superimposed to a power law in the decay of the magnetization and its logarithmic derivative and also from the dependence of the critical exponents on the segmentation step. These oscillations are discussed in the framework of the discrete scale invariance of the substrate and carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The exponent $\theta$ of the initial increase in the magnetization was also obtained and the results suggest that it would be almost independent of the fractal dimension of the susbstrate, provided that $d_H$ is close enough to d=2.Comment: 9 figures, 3 tables, 10 page

Electric-Field Gradient at Cd Impurities in In2o3. A FLAPW Study

We report an ab initio study of the electric-field gradient tensor (EFG) at Cd impurities located at both inequivalent cationic sites in the semiconductor In2O3. Calculations were performed with the FLAPW method, that allows us to treat the electronic structure of the doped system and the atomic relaxations introduced by the impurities in the host lattice in a fully self-consistent way. From our results for the EFG (in excellent agreement with the experiments), it is clear that the problem of the EFG at impurities in In2O3 cannot be described by the point-charge model and antishielding factors.Comment: 4 pages, 2 figures, and 2 table

Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

The T=0 dynamical properties of the one-dimensional (1D) $s=1/2$ Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe ansatz for cyclic chains of $N$ sites. The ground state at magnetization $0<M_z<N/2$, which can be interpreted as a state with $2M_z$ spinons or as a state of $M_z$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the {\em psinons} and {\em antipsinons}. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of lineshapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF$_3$, Cu(C$_4$H$_4$N$_2)(NO_3)_2$, and CuGeO$_3$.Comment: 13 pages, 12 figure