Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Spontaneous Magnetization and Electron Momentum Density in 3D Quantum Dots

We discuss an exactly solvable model Hamiltonian for describing the interacting electron gas in a quantum dot. Results for a spherical square well confining potential are presented. The ground state is found to exhibit striking oscillations in spin polarization with dot radius at a fixed electron density. These oscillations are shown to induce characteristic signatures in the momentum density of the electron gas, providing a novel route for direct experimental observation of the dot magnetization via spectroscopies sensitive to the electron momentum density.Comment: 5 pages (Revtex4), 4 (eps) figure

On the Crustal Matter of Magnetars

We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of Thomas-Fermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter. The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered. Conventional Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used for the nuclear mass formula. A lot of significant changes in the characteristic properties of dense crustal matter, both at the outer crust and the inner crust, have been observed.Comment: 29 pages REVTEX manuscript, 15 .eps figures (included

Optical properties in the Cu fused silica system irradiated with swift heavy ions

Swift heavy ions are used to study the effects of electronic energy loss oil Cu cluster formation in fused silica after post-irradiation annealing. Fused silica substrates covered with 10 run thin Cu-films were irradiated using beams of either 120 MeV Ag9+ ions or 350 MeV Au26+ ions at fluences ranging from 2 x 10(13) to 1 X 10(14) cm(-2). After irradiation, the samples were annealed for 30 min in argon, at temperatures of 773-1200 K and characterized by UV-VIS absorption spectroscopy. The swift ion irradiations created E' and B-2 defects in silica, which were partially eliminated during annealing. In addition, Cu cluster formation in silica was observed after annealing. Irradiation fluences exceeding 4 x 10(13) cm(-2) and annealing temperatures above 1100 K are more effective in forming larger nanoclusters. (c) 2005 Elsevier B.V. All rights reserved

Measurement of hadron and lepton-pair production at 130 GeV<root s<140 GeV at LEP

Contains fulltext : 26240.pdf (publisher's version ) (Open Access

Search for the Decays B-D(0)-]Gamma-Gamma and B-S(0)-]Gamma-Gamma

Contains fulltext : 26235.pdf (publisher's version ) (Open Access