On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions

The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation function can be used as building block for computing various (both local and nonlocal) correlation functions in the model. The row configuration probability is calculated using the quantum inverse scattering method; the final result is given in terms of a multiple integral. The connection with the emptiness formation probability, another nonlocal correlation function which was computed elsewhere using similar methods, is also discussed.Comment: 15 pages, 2 figure

Functional relations for the six vertex model with domain wall boundary conditions

In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied for small lattices and the properties determining the partition function are also discussed.Comment: 19 pages, v2: typos corrected, new section and appendix added. v3: minor corrections, to appear in J. Stat. Mech

The arctic curve of the domain-wall six-vertex model

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of $q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction

Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1) a peculiar form of interaction of the system as a whole with the external gauge fields; 2) a modification of the dynamical part of the symmetry transformations, which is needed to take into account the alteration of the dynamics itself, induced by the {\it gauge} fields. In particular, the Yang-Mills fields associated to the internal rotations have the effect of modifying the time derivative of the internal variables in a scheme of minimal coupling (introduction of an internal covariant derivative); 3) given their dynamical effect, the Yang-Mills fields associated to the internal rotations apparently define a sort of Galilean spin connection, while the Yang-Mills fields associated to the quadrupole momentum and to the internal energy have the effect of introducing a sort of dynamically induced internal metric in the relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty available at: http://www.iop.org/). The file is available at: http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip file with the IOP preprint style include

Solving the Frustrated Spherical Model with q-Polynomials

We analyse the Spherical Model with frustration induced by an external gauge field. In infinite dimensions, this has been recently mapped onto a problem of q-deformed oscillators, whose real parameter q measures the frustration. We find the analytic solution of this model by suitably representing the q-oscillator algebra with q-Hermite polynomials. We also present a related Matrix Model which possesses the same diagrammatic expansion in the planar approximation. Its interaction potential is oscillating at infinity with period log(q), and may lead to interesting metastability phenomena beyond the planar approximation. The Spherical Model is similarly q-periodic, but does not exhibit such phenomena: actually its low-temperature phase is not glassy and depends smoothly on q.Comment: Latex, 14 pages, 2 eps figure

Asymptotics and functional form of correlators in the XX - spin chain of finite length

We verify the functional form of the asymptotics of the spin - spin equal - time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization also predicts the functional form of the correlators for the chains of finite length. We found the exact expression for the spin- spin equal- time correlator on finite lattice. We find the excellent agreement of the exact correlator with the prediction given by the leading asymptotics result up to the very small distances. We also establish the correspondence between the value of the constant before the asymptotics for the XX- chain with the expression for this constant proposed by Lukyanov and Zamolodchikov. We also evaluate the constant corresponding to the subleading term in the asymptotics in a way which is different from the previous studies.Comment: LaTex, 12 page

Towards a framework for work package allocation for GSD

Proceeding of: Proceeding of: OTM 2011 Workshops: Confederated International Workshops and Posters: EI2N+NSF ICE, ICSP+INBAST, ISDE, ORM, OTMA, SWWS+MONET+SeDeS, and VADER 2011, Hersonissos, Crete, Greece, October 17-21, 2011Global software development is an inexorable trend in the software industry. The impact of the trend in conventional software development can be found in many of its aspects. One of them is task or work package allocation. Task allocation was traditionally driven by resource competency and availability but GSD introduces new complexities to this process including time-zones differences, costs and cultural differences. In this work a report on the construction of a framework for work-package allocation within GSD projects is presented. This framework lies on three main pillars: individual and organizational competency, organizational customization and sound assessment methods.This work is supported by the Spanish Centro para el Desarrollo Tecnológico Industrial (CDTI) under the Eureka Project E! 6244 PROPS-Tour and the national cooperation project SEM-IDi (IDI-20091150)

Solving Gauss' Laws and Searching Dirac Observables for the Four Interactions

A review is given of the status of the program of classical reduction to Dirac's observables of the four interactions (standard SU(3)xSU(2)xU(1) particle model and tetrad gravity) with the matter described either by Grassmann-valued fermion fields or by particles with Grassmann charges.Comment: 9 pages, LaTeX (using espcrc2.sty). Talk given at the Second Conf. on Constrained Dynamics and Quantum Gravity, S.Margherita Ligure, 17-21 September 199

Area versus Length Distribution for Closed Random Walks

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area, on a hypercubic lattice, in the limit of infinite number of dimensions. The formula is investigated in detail, and asymptotic behaviours are evaluated. The area distribution in the limit of long loops is computed. As a byproduct, we obtain also an infinite set of new, nontrivial identities.Comment: 17 page

Dynamics of spin correlations in the spin-1/2 isotropic XY chain in a transverse field

Dynamic xx spin pair correlation functions for the isotropic spin-1/2 XY chain are calculated numerically for long open chains in the presence of a transverse magnetic field at finite temperature. As an application we discuss the temperature dependence of the spin-spin relaxation time in PrCl_3.Comment: 2 pages, latex, 2 figures, abstract of the paper presented at Ampere Summer School ``Applications of Magnetic Resonance in Novel Materials'' Nafplion, Greece, 3-9 September, 2000, partially published in J. Phys. A: Math. Gen. 33, 3063 (2000