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.Comment: 16 pages,cmp209.sty (included), 9 postscript figures, author information under http://www.physik.uni-leipzig.de/index.php?id=2

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 $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $\gamma =1.305(5)$ at the random fixed point.Comment: 16 pages, 10 figure

Interaction dependence of composite fermion effective masses

We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3, 2/5 and 3/7 show that m_eff \sim \alpha^{-1}.Comment: 4 pages, RevTeX, 5 figure

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 4-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 {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.Comment: 8 pages, 6 figure

Unpolarized quasielectrons and the spin polarization at filling fractions between 1/3 and 2/5

We prove that for a hard core interaction the ground state spin polarization in the low Zeeman energy limit is given by $P=2/\nu-5$ for filling fractions in the range $1/3 \leq\nu\leq 2/5$. The same result holds for a Coulomb potential except for marginally small magnetic fields. At the magnetic fields $B<20T$ unpolarized quasielectrons can manifest themselves by a characteristic peak in the I-V characteristics for tunneling between two $\nu=1/3$ ferromagnets.Comment: 8 pages, Latex. accepted for publication in Phys.Rev.

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. 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 explicitly 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.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replace

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 3-dimensional gauge coupling approaches a finite $\lambda$ dependent value at the critical temperature. The $\lambda$ (Higgs mass) dependence of the 1-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 mass is small compared to the W mass. To 1-loop accuracy, there is no Higgs mass range compatible with experimental limits where washing-out of a B+L asymmetry could be avoided for the minimal standard model with one Higgs doublet.Comment: 17 pages, RevTeX, (4 figures in a separate uuencoded file), HD-THEP-93-23re