We investigate a generalized nonlinear O(3) model in three space dimensions where the fields are maps from R 3 ഫ͕ϱ͖ to 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 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. ͓S0556-2821͑97͒00520-1͔

In order to study the influence of quenched disorder on second-order phase transitions, hightemperature series expansions of the susceptibility 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 susceptibility to be γ = 1.305 (5)

We review and compare different approaches for studying the influence of quenched, random disorder in three-dimensional Ising and Potts models for ferromagnets subject to impurities. From a theoretical view point, field theoretic renormalization group studies provide quite accurate results. Experiments carried out on crystalline mixtures of compounds lead to measurements of criticial exponents as accurate as three digits. Numerically, extensive Monte Carlo simulations are shown to be of comparable accuracy. Finally, we also discuss recently generated high-temperature series expansions for the free energy and susceptibility. Within this approach, using the star-graph expansion technique, quenched disorder averages can be calculated exactly while keeping the disorder strength p as well as the dimension d as symbolic parameters.

The vacuum energy of a scalar field in a spherically symmetric background field is considered. Based on previous work [Phys. Rev. D 53 (1996) 5753], 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.

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1qubit maps are presented. We construct the relevant convex roof patterns by a new method. We conclude that two component optimal decompositions always exist.Our results can be transferred to 2 × n-quantum systems providing the concurrence for all rank two density operators as well as lower and upper bounds for their entanglement of formation.We apply these results to a study of the entanglement entropy of 1-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we analyze the bifurcation patterns appearing in the convex roof of optimal decompositions and give results for the one-shot (Holevo-Schumacher-Westmoreland) capacity of those maps.

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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 Z D for arbitrary values of q. The series are up to order 20 for dimension D ≤ 3, order 19 for D ≤ 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 γ 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 .

We study Haldane's and Jain's 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 3and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.