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Exact calculations are presented for the ground state of linear antiferromagnetic Heisenberg chains with open ends. The wave function and the energy are given for chains with N = 4, 6, and 8, and quantum number S = 1/2. It is shown that in the limit for N - ∞ the ground state is probably nondegenerate and the long-range order tends to zero. The short-range order shows a strongly oscillating character due to end effects persisting over relatively long distances. A comparison with closed rings ...
A description is given of the anomalous skin effect in a cylinder placed in an a.c. magnetic field parallel to the cylinder axis. The necessary nonlocal relation between current density and electric field inside the sample is established with the aid of Boltzmann's transport equation. Results are presented in terms of the current density in the sample and its magnetic susceptibility.
The induced response of a cylindrical conductor due to a sinusoidal magnetic field parallel to the axis of the cylinder can be obtained from the azimuthal components of the induced electrical fields or currents. In case mean free path effects of the électrons have to be considered the values of these electrical fields or currents are governed by integral equations. A numerical solution method for these integral equations is presented.
An approximate value for the ground-state energy of an antiferromagnetic lattice of spins one-half is determined by means of a repeated renormalization procedure in which the lattice is divided into cells with an effective interaction. This effective interaction is determined on the basis of the spin-hamiltonian formalism.
The inductive response of type II superconductors to applied fields with trapezoidal time dependence is described for samples with a slab geometry. An extension of the critical state model which accounts for the observed waveform of the voltage, induced in the pick-up coil, is given. Typical experiments on Nb-slabs with weak pinning and flux flow in fields with both small and large amplitudes are reported.
A renormalization procedure gives rigorous upper bound for the ground-state energy per spin for the triangular antiferromagnetic lattice with Heisenberg interaction.
Complete sets of diagonal operators, i.e. operators commuting with the hamiltonian of a physical system, are constructed. In terms of these sets all diagonal operators can be written as a series, the uniform convergence of which is studied for infinitely large systems. This uniform convergence is introduced as a possible criterion for ergodicity.
The inductive response of metals to applied fields with trapezoidal time dependence is described for samples with cylindrical geometry and for slabs. The influence of coil effects and magnetoresistance is accounted for but mean free path and surface effects are ignored. Experimental data obtained for tin show a close agreement with the theoretical predictions.
Using a Wannier function approach and a transformation of the coordinate system it is shown that a method can be set up to calculate the scattered wave function of a dislocated lattice.
A renormalization procedure gives a rigorous upper bound for the ground-state energy per spin for a Peierls-distorted antiferromagnetic chain with Heisenberg interaction.