Meik Hellmund

Static solitons with nonzero Hopf number

We investigate a generalized nonlinear O(3) {sigma} model in three space dimensions where the fields are maps from R{sup 3}{union}{l_brace}{infinity}{r_brace} to S{sup 2}. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We numerically compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons. {copyright} {ital 1997} {ital The American Physical Society}

Star-graph expansions for bond-diluted Potts models

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the (p,d) parameter space for any value of q. For the bond-diluted four-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent gamma as a function of p as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data [Chatelain et al., Phys. Rev. E 64, 036120 (2001)] shows signals for the softening to a second-order transition at finite disorder strength.

The decay of the sphaleron

Abstract Baryon number violation in the electroweak standard model is expected to proceed through classical transitions over the sphaleron barrier connecting vacua of different Chern-Simons number. The required energy is the order of 10 TeV. The event structure is studied in this paper by following the real-time evolution of the sphaleron field configuration. On average, the sphaleron is found to decay into 42 W-bosons and 8 Higgs particles, if the Higgs mass is close to the W-boson mass.

Dependence of the vacuum energy on spherically symmetric background fields

The vacuum energy of a scalar field in a spherically symmetric background field is considered. Based on previous work [hep-th/9608070], the numerical procedure is refined further and applied to several examples. We provide numerical evidence that repulsive potentials lead to positive contributions to the vacuum energy. Furthermore, the crucial role played by bound-states is clearly seen.

Random-bond Potts models on hypercubic lattices: high-temperature series expansions*

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic parameters. This allows us to scan large regions of the (p, d) parameter space for any value of q. For the bond-diluted 4-state Potts model in three dimensions we present first results for the critical temperature as a function of p as obtained from the analysis of susceptibility series up to order 18.

High-temperature series expansions for random Potts models

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.

COMPARISON OF FRACTIONAL-QUANTUM-HALL-EFFECT QUASIELECTRON TRIAL WAVE FUNCTIONS ON A SPHERE

We study Haldanes and Jains proposals for the quasiparticle wave function on the sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.

High-temperature series expansions for the q-state Potts model on a hypercubic lattice and critical properties of percolation.

We present results for the high-temperature series expansions of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice ZD for arbitrary values of q. The series are up to order 20 for dimension D<or=3, order 19 for D<or=5, and up to order 17 for arbitrary D. Using the q-->1 limit of these series, we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of q up to order D-9.

Sphaleron effects near the critical temperature

We discuss one-loop radiative corrections to the sphaleron-induced baryon-number-violating transition rate near the electroweak phase transition in the standard model. We emphasize that in the case of a first-order transition a rearrangement of the loop expansion is required close to the transition temperature. The corresponding expansion parameter, the effective three-dimensional gauge coupling, approaches a finite [lambda]-dependent value at the critical temperature. The [lambda] (Higgs boson mass) dependence of the one-loop radiative corrections is discussed in the framework of the heat kernel method. Radiative corrections are small compared to the leading sphaleron contribution as long as the Higgs boson mass is small compared to the [ital W] mass. To one-loop accuracy, there is no Higgs boson mass range compatible with experimental limits where washing out of a [ital B]+[ital L] asymmetry could be avoided for the minimal standard model with one Higgs doublet.

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in