18 research outputs found
Evidence for a Critical Behavior in Pure Compact QED
We present evidence about a critical behavior of compact QED (CQED) pure
gauge theory. Regularizing the theory on lattices homotopic to a sphere, we
present evidence for a critical, i.e. second order like behavior at the
deconfinement phase transition for certain values of the coupling parameter
.Comment: 3 pages, 3 figures, POSTSCRIPT file (127KB uuencoded
More on random-lattice fermions
The lattice fermion determinants, in a given background gauge field, are
evaluated for two different kinds of random lattices and compared to those of
naive and wilson fermions in the continuum limit. While the fermion doubling is
confirmed on one kind of lattices, there is positive evidence that it may be
absent for the other, at least for vector interactions in two dimensions.
Combined with previous studies, arbitrary randomness by itself is shown to be
not a sufficient condition to remove the fermion doublers.Comment: 3 pages, uuencoded compress postscript, contributed poster at the
Lattice '94 Symposiu
Spin and Gauge Systems on Spherical Lattices
We present results for 2D and 4D systems on lattices with topology homotopic
to the surface of a (hyper) sphere or . Finite size scaling is
studied in situations with phase transitions of first and second order type.
The Ising and Potts models exhibit the expected behaviour; for the 4D pure
gauge theory we find consistent scaling indicative of a second order
phase transition with critical exponent .Comment: 4 pages, LaTeX, 3 POSTSCRIPT figures (uuencoded
Correlations in the Sine-Gordon Model with Finite Soliton Density
We study the sine-Gordon (SG) model at finite densities of the topological
charge and small SG interaction constant, related to the one-dimensional
Hubbard model near half-filling. Using the modified WKB approach, we find that
the spectrum of the Gaussian fluctuations around the classical solution
reproduces the results of the Bethe ansatz studies. The modification of the
collective coordinate method allows us to write down the action, free from
infra-red divergencies. The behaviour of the density-type correlation functions
is non-trivial and we demonstrate the existence of leading and sub-leading
asymptotes. A consistent definition of the charge-raising operator is
discussed. The superconducting-type correlations are shown to decrease slowly
at small soliton densities, while the spectral weight of right (left) moving
fermions is spread over neighboring "4k_F" harmonics.Comment: 12 pages, 3 eps figures, REVTEX; a discussion of fermions is adde
Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes
We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces