Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.Comment: 12 pages, 14 figure

Vortex behavior near a spin vacancy in 2D XY-magnets

The dynamical behavior of anisotropic two dimensional Heisenberg models is still a matter of controversy. The existence of a central peak at all temperatures and a rich structure of magnon peaks are not yet understood. It seems that the central peaks are related, in some way, to structures like vortices. In order to contribute to the discussion of the dynamical behavior of the model we use Monte Carlo and spin dynamics simulations as well analytical calculations to study the behavior of vortices in the presence of nonmagnetic impurities. Our simulations show that vortices are attracted and trapped by the impurities. Using this result we show that if we suppose that vortices are not very much disturbed by the presence of the impurities, then they work as an attractive potential to the vortices explaining the observed behavior in our simulations.Comment: 4 pages, 6 figure

Green's function approach to the magnetic properties of the kagome antiferromagnet

The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions are obtained and characterize this system as a two-dimensional quantum spin liquid. Spin-spin correlation functions decay exponentially with distance down to low temperature and the calculated missing entropy at T=0 is found to be $0.46\ln{2}$. Within the present scheme, the specific heat exhibits a single peak structure and a $T^2$ dependence at low temperature.Comment: 6 (two-column revtex4) pages, 5 ps figures. Submitted to Phys. Rev.

Spin-dynamics simulations of the triangular antiferromagnetic XY model

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L \leq 300$. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S({\bf q},w)$ for momentum ${\bf q}$ and frequency $\omega$. Below $T_{KT}$(Kosterlitz-Thouless transition), both the in-plane ($S^{xx}$) and the out-of-plane ($S^{zz}$) components of $S({\bf q},\omega)$ exhibit very strong and sharp spin-wave peaks. Well above $T_{KT}$, $S^{xx}$ and $S^{zz}$ apparently display a central peak, and spin-wave signatures are still seen in $S^{zz}$. In addition, we also observed an almost dispersionless domain-wall peak at high $\omega$ below $T_{c}$(Ising transition), where long-range order appears in the staggered chirality. Above $T_{c}$, the domain-wall peak disappears for all $q$. The lineshape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z$ = 1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequeny $\omega_{m}$ and the dynamic structure factor $S({\bf q},\omega)$ itself.Comment: 8 pages, RevTex, 10 figures, submitted to PR

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Range extensions along western Atlantic for Epialtidae crabs (Brachyura, Majoidea) genera Acanthonyx Latreille, 1828 and Epialtus H. Milne Edwards, 1834

The present study provided information extending the known geographical distribution of three species of majoid crabs, the epialtids Acanthonyx dissimulatus Coelho, 1993, Epialtus bituberculatus H. Milne Edwards, 1834, and E. brasiliensis Dana, 1852. Specimens of both genera from different carcinological collections were studied by comparing morphological characters. We provide new data that extends the geographical distributions of E. bituberculatus to the coast of the states of Paraná and Santa Catarina (Brazil), and offer new records from Belize and Costa Rica. Epialtus brasiliensis is recorded for the first time in the state of Rio Grande do Sul (Brazil), and A. dissimulatus is reported from Quintana Roo, Mexico. The distribution of A. dissimulatus, previously known as endemic to Brazil, has a gap between the states of Espírito Santo and Rio de Janeiro. However, this restricted southern distribution is herein amplified by the Mexican specimens

Collider aspects of flavour physics at high Q

This review presents flavour related issues in the production and decays of heavy states at LHC, both from the experimental side and from the theoretical side. We review top quark physics and discuss flavour aspects of several extensions of the Standard Model, such as supersymmetry, little Higgs model or models with extra dimensions. This includes discovery aspects as well as measurement of several properties of these heavy states. We also present public available computational tools related to this topic.Comment: Report of Working Group 1 of the CERN Workshop ``Flavour in the era of the LHC'', Geneva, Switzerland, November 2005 -- March 200

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

PACS. 75.10.Hk Classical spin models – 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.),