Critical properties of the XXZ model with long-range interactions on the double chain

The $XXZ$ model $(s = 1/2)$ in a transverse field on a double chain with a uniform long-range interaction among the $z$ components of the spins is considered. The nearest-neighbour interactions are restricted to the components in the $xy$ plane and to the spins within the same chain leg, such that the Hamiltonian is given by $H = -\sum_{m=1}^{2} J_{m} \sum_{j=1}^{N}(S_{m,j}^{x}S_{m, j+1}^{x} + S_{m,j}^{y}S_{m,j+1}^{y}) - \frac{I}{N}\sum_{m,n=1}^{2} \sum_{j,k=1}^{N}S_{m,j}^{z}S_{n,k}^{z}-h\sum_{m=1}^{2} \sum_{j=1}^{N}S_{m,j}^{z}$, where $N$ is the number of sites of the lattice and $m,n$ $(m,n = 1, 2)$ label the chain legs. The model is solved exactly by introducing the Jordan-Wigner and integral Gaussian transformations, which map the Hamiltonian in a non-interacting fermion system and corresponds to an extension of the model recently studied by the authors for a single chain. The equation of state is obtained in closed form, and the critical classical (at $T > 0$) and quantum (at $T = 0$) behaviours can be determined exactly. The quantum critical surface is determined in the space generated by the transverse field and interaction parameters, and the crossover lines separating the different critical regimes are also obtained. It is also shown that, differently from the results obtained for the single chain, the system can present multiple quantum transitions.Comment: 02 pages, 02 figures, to appear in JMMM (Proceedings of ICM2006

Leavitt Path algebras via partial skew ring theory

We will introduce the theory or partial actions of groups and their associated algebras. As an example we will realize the Leavitt path algebra associated with a graph as a partial skew group ring. To finish, we will show how some of the results regarding Leavitt path algebras may be obtained from general results regarding partial skew ring theory.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

The delphi technique applied to urban and cultural tourism research in the Algarve

O turismo urbano é hoje uma actividade económica e social principal, e a componente cultural das cidades é um dos factores principais para a atracção de visitantes. O presente trabalho resulta da investigação desenvolvida no mbito da dissertação de mestrado que estabeleceu como bjectivos principais avaliar a importância do turismo cultural nas cidades de Faro e Silves, numa abordagem pela oferta, e propor ormas de prever o desenvolvimento das actividades associadas a esse tipo de turismo para o futuro. A “tranversalidade” do conhecimento ligado ao turismo, e as dinâmicas que pode criar, tornam o turismo, uma das actividades mais difíceis de quantificar e avaliar. A investigação desenvolvida pode ser traduzida numa abordagem integradora do conceito de património cultural e de turismo urbano, domínios que até recentemente têm permanecido separados. A utilização de vários métodos de investigação de forma complementar – entrevistas de grupo, método Delphi e estudo de caso – revelou-se um ponto forte da metodologia adoptada. Por outro lado, como será demonstrado, a técnica Delphi, ainda que tenha revelado algumas dificuldades na sua aplicação, e não se constituindo como um instrumento de decisão principal, nem tendo sido com frequência utilizado no turismo, demonstrou-se muito adequado para o tratamento de informação qualitativa. Assim, apresentam-se as principais técnicas de investigação utilizadas na nossa pesquisa e analisam-se os vários métodos disponíveis à investigação em turismo. Alguns dos resultados adquiridos serão também sumariados nos estudos de caso, demonstrando o potencial que a utilização conjunta de vários métodos de pesquisa trouxe para a resposta aos objectivos propostos.Urban tourism is a major economic and social activity where the cultural dimension of cities is one of the main factors that attract visitors. The present work results from a dissertation thesis that aimed to evaluate the existence of cultural tourism in the towns of Faro and Silves and proposed means of fostering such activities in the future. The “transversality” of knowledge linked to tourism and the dynamics it can create make tourism one of the most difficult activities to quantify and evaluate. The developed investigation can be translated into an integrating approach of the concept of cultural patrimony and urban tourism, domains that so far have stayed apart. The use of several investigative methods in a complementary way – group interviews, Delphi method and case study (three sided methods) –, have revealed to be a strong point in the applied methodology. On the other hand, as will be shown later, the Delphi technique, although revealing some difficulties of application, and not being a decisive instrument nor being often used in tourism, has been very useful for the treatment of qualitative information. So we will introduce the main methodologies used on our research and analyse the various methods available for tourism research. Some of the acquired results are also summarized and specified in the case studies, highlighting the potential that the combination of several investigative methods have brought in helping to discover the answer to proposed aimsinfo:eu-repo/semantics/publishedVersio

A Point Counting Algorithm for Cyclic Covers of the Projective Line

We present a Kedlaya-style point counting algorithm for cyclic covers $y^r = f(x)$ over a finite field $\mathbb{F}_{p^n}$ with $p$ not dividing $r$, and $r$ and $\deg{f}$ not necessarily coprime. This algorithm generalizes the Gaudry-G\"urel algorithm for superelliptic curves to a more general class of curves, and has essentially the same complexity. Our practical improvements include a simplified algorithm exploiting the automorphism of $\mathcal{C}$, refined bounds on the $p$-adic precision, and an alternative pseudo-basis for the Monsky-Washnitzer cohomology which leads to an integral matrix when $p \geq 2r$. Each of these improvements can also be applied to the original Gaudry-G\"urel algorithm. We include some experimental results, applying our algorithm to compute Weil polynomials of some large genus cyclic covers

Orthogonal Polynomials and Sharp Estimates for the Schr\"odinger Equation

In this paper we study sharp estimates for the Schr\"odinger operator via the framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer polynomials to prove a new weighted inequality for the Schr\"odinger equation that is maximized by radial functions. We use Hermite and Laguerre polynomial expansions to produce sharp Strichartz estimates for even exponents. In particular, for radial initial data in dimension 2, we establish an interesting connection of the Strichartz norm with a combinatorial problem about words with four letters.Comment: 22 page