One Spin Trace Formalism for BK B_K

It has been known for some time that there are two methods to calculate $B_K$ with staggered fermions: one is the two spin trace formalism and the other is the one spin trace formalism. Until now, the two spin trace formalism has been exclusively used for weak matrix element calculations with staggered fermions. Here, the one spin trace formalism to calculate $B_K$ with staggered fermions is explained. It is shown that the one spin trace operators require additional chiral partner operators in order to keep the continuum chiral behavior. The renormalization of the one spin trace operators is described and compared with the two spin trace formalism.Comment: 47 pages, latex, 4 figures are available on reques

The Chiral Phase Transition in Dissipative Dynamics

Numerical simulations of the chiral phase transition in the (3+1)dimensional O(4)-model are presented. The evolutions of the chiral field follow purely dissipative dynamics, starting from random chirally symmetric initial configurations down to the true vacuum with spontaneously broken symmetry. The model stabilizes topological textures which are formed together with domains of disoriented chiral condensate (DCC) during the roll-down phase. The classically evolving field acts as source for the emission of pions and $\sigma$ mesons. The exponents of power laws for the growth of angular correlations and for emission rates are extracted. Fluctuations in the abundance ratios for neutral and charged pions are compared with those for uncorrelated sources as potential signature for the chiral phase transition after heavy-ion collisions. It is found that the presence of stabilizing textures (baryons and antibaryons) prevents sufficiently rapid growth of DCC-domain size, so observability of anomalous tails in the abundance ratios is unlikely. However, the transient formation of growing DCC domains causes sizable broadening of the distributions as compared to the statistical widths of generic sources.Comment: 28 pages, 8 figure

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient

Sub-bandgap absorption spectroscopy and minority carrier transport properties of hydrogenated microcrystalline silicon thin films

Hydrogenated microcrystalline silicon thin films have been prepared using HW-CVD and VHF-PECVD techniques with different silane concentrations. The steady-state photoconductivity, dual beam photoconductivity, photothermal deflection spectroscopy and steady-state photocarrier grating (SSPG) methods have been used to investigate the optical and electronic properties of the films. Two different sub-bandgap absorption methods have been applied and analyzed to obtain a better insight into the electronic states involved. For some films, differences existed in the optical absorption spectra when the measurements were carried out through the film side and through the substrate side. In addition, for some films, fringe patterns remained on the spectrum after the calculation of the fringe free absorption spectrum, which indicates that structural inhomogeneities were present throughout the film. Finally, minority carrier diffusion lengths deduced from the SSPG measurements were investigated as a function of the crystalline volume fraction (I-c(RS)) obtained from Raman spectroscopy. The longest diffusion lengths and lowest sub-bandgap absorption coefficients were obtained for films deposited in the region of the transition to the amorphous growth