Quantum model of interacting " strings " on the square lattice Abstract The model which is the generalization of the one-dimensional XY-spin chain for the case of the two-dimensional square lattice is considered. The subspace of the " string " states is studied. The solution to the eigenvalue problem is obtained for the single " string " in cases of the " string " with fixed ends and " string "...

We consider equations on the monoid of factorial languages on the binary alphabet. We use the notion of a canonical decomposition of a factorial language and previous results by Avgustinovich and the author to solve several simple equations on binary factorial languages including Xn = Y n, the commutation equation XY = Y X and the conjugacy equation XZ = ZY . At the end of the paper we discuss ...

The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.

We use the three dimensional uniformly frustrated XY model as a model for a high temperature superconductor in an applied magnetic field and explicitly measure the longitudinal correlation length jz in the vortex line liquid phase. We determine the scaling of jz with magnetic field and system anisotropy close to the vortex lattice melting transition. We apply our results to determine the extent...

The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY , where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, . . . A 4 appears for the first time at position 220, but a 5 does not appear until about position 1010 23 . The main result...

We show that a generalized Landau theory for the smectic A and C phases exhibits a biaxiality induced AC tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the AC transition is 3D XY like, while for sufficiently small orientational order, it is either tricritical or 1st order. We investiga...

The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.

For two (possibly stochastically dependent) random variables X and Y taking values in {O, ... , m 1} we study the distribution of the random residue U = XY mod m. In the case of independent and uniformly distributed X and Y we provide an exact solution in terms of generating functions that are computed via p-adic analysis. We show also that in the uniform case it is stochastically smaller than ...

A simple but accurate mesh current analysis is performed on a XY model and on a SIMF model to derive the equations for a Josephson junction array. The equations obtained here turn out to be different from other equations already existing in the literature. Moreover, it is shown that the two models come from a unique hidden structure. ∗e-mail address: [email protected] ∗∗revised on May,...