Simón Bolívar University

About: Simón Bolívar University is a education organization based out in Caracas, Venezuela. It is known for research contribution in the topics: Population & Crystallization. The organization has 5912 authors who have published 8294 publications receiving 126152 citations.

Symmetric functions in noncommuting variables

Abstract: Consider the algebra Q >of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x 1 , x 2 ,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as well as investigating their properties.

Critical behavior of the two-dimensional XY model: A Monte Carlo simulation.

Abstract: We have performed Monte Carlo (MC) simulations on systems of L\ifmmode\times\else\texttimes\fi{}L classical planar unit spins on square lattices, for L=6, 15, 30, 60, 90, and 200. The interaction between any two given spins S${\ensuremath{\rightarrow}}_{1}$ and S${\ensuremath{\rightarrow}}_{2}$ is given by -JS${\ensuremath{\rightarrow}}_{1}$\ensuremath{\cdot}S${\ensuremath{\rightarrow}}_{2}$ if ${S}_{1}$ and ${S}_{2}$ are nearest neighbors and vanishes otherwise. In order to make sure that our results correspond to equilibrium values, we have looked into the time-dependent properties of this model in the vicinity of critical temperature (${T}_{c}$). We have found that the diffusion constant for vortex motion is given at ${T}_{c}$ by D\ensuremath{\simeq}0.2 (in units of nearest-neighbor distance squared per MC step per spin). The values of the relaxation times follow from the value of D. Our computer running times were typically ${10}^{5}$ MC steps per spin, larger than any relaxation time for the system sizes we deal with. We use a procedure based on finite-size scaling to establish the value of ${T}_{c}$=0.89J/${k}_{B}$, the value of \ensuremath{ u}=0.5\ifmmode\pm\else\textpm\fi{}0.1, and the value of ${\ensuremath{\eta}}_{c}$=0.24\ifmmode\pm\else\textpm\fi{}0.03, in agreement with the values predicted by the Kosterlitz-Thouless theory.