Simple classical spin models well-known to physicists as the ANNNI and Heisenberg XY Models. in which long-range interactions occur in a pattern given by the Mexican Hat operator. can generate many of the structural properties characteristic of the ocular dominance columns and iso-orientation patches seen in cat and primate visual cortex.

this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

We present the algebraic Bethe Ansatz solution for the vertex model recently proposed by Zhou [5] as the classical analog of the Bariev interacting XY chains. The relevant commutation rules between the creation fields contain the Hecke symmetry pointed out recently by Hikami and Murakami [6]. The eigenvalues of the corresponding transfer matrix are explicitly given.

The thermodynamical property of a small cluster including M Hubbard dimers, each of which is described by the two-site Hubbard model, has been discussed within the nonextensive statistics (NES). We have calculated the temperature dependence of the energy, entropy, specific heat and susceptibility for M = 1, 2, 3 and ∞ (corresponding to q = 1), assuming the relation between the entropic index q ...

We develop a Bayesian method for nonparametric model–based quantile regression. The approach involves flexible Dirichlet process mixture models for the joint distribution of the response and the covariates, with posterior inference for different quantile curves emerging from the conditional response distribution given the covariates. An extension to allow for partially observed responses leads ...

In the ordered phase of 2D XY ferromagnet the dipole force induce a strong interaction between spin-waves in the long wavelength limit. This interaction leads to the transformation of the spin-wave excitation into a new soft-mode excitation in an intermediate range of wavelengths limited in magnitude and direction; and into an anomalous anisotropic diffusion mode excitation at long wavelengths....

In recent works [1] (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2DXY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size, below the Kosterlitz-Thoules temperature. However, the ...

For graphs with maximum degree A and diameter D, an upper bound on the number of vertices is 1 + AxF:-,‘(A 1)‘. This bound is called the Moore bound for graphs and the graphs that attain it are called Moore graphs. Similar bounds for directed graphs and for hypergraphs have been defined and the existence of directed Moore graphs and of Moore hypergraphs has been studied. In this article, we def...

Dynamics of a Local Perturbation in the XY Mode!. I-Approach to Equilibrium D. B. Abraham§, E. Barouch∗§, G. Gallavotti and A. Martin-Löf Abstract: The magnetization and spin correlation functions of theX−Y model are analysed exactly when the system is subjected to a local perturbation of the magnetic field in the z-direction. When such a perturbation is removed, these quantities approach their...

Equation Basepoint Parameter Dimension Restrictions of Isotropy #1 W = XY + Z (0, 0, 0, 0) 4 #2 W 2 = XY + Z + 1 (1, 0, 0, 0) 3 #3 W = XY + Z +X (0, 0, 0, 0) 2 #4 W = XY + Z +XZ + αX (0, 0, 0, 0) α arbitrary 1 #5 W = XY + Z +XZ (0, 0, 0, 0) 1 #6 W 2 = XY +XY +XZ (1, 1, 0, 1) 1 #7 W = XY + Z (1, 0, 0, 1) α 6= 0, 1, 2 1 #8 W = XY + e (1, 0, 0, 0) 1 #9 W = XY + logZ (0, 0, 0, 1) 1 #10 W = XY + Z l...