Ground-State Properties of Finite Antiferromagnetic Chains

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 is made and the connection with the observation of a reduction of the zero-point deviation in the neighbourhood of non-magnetic impurities in more-dimensional systems is pointed out

Anomalous skin effect in cylindrical samples

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 response of metals in trapezoidal magnetic fields

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

Scattered wave functions of dislocated lattices

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

The response of type H superconductors to trapezoidal magnetic fields

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

The determination of the ground-state energy of an antiferromagnetic lattice by means of a renormalization procedure

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

An exact upper bound for the ground-state energy of the triangular antiferromagnetic lattice by means of a renormalization procedure

A renormalization procedure gives rigorous upper bound for the ground-state energy per spin for the triangular antiferromagnetic lattice with Heisenberg interaction

An upper bound for the ground-state energy of an antiferromagnetic chain with next-nearest-neighbor interaction

A trial function for the ground state of the antiferromagnetic linear chain leads to an equation for an upper bound of the ground-state energy per spin. This equation is solved exactly

Complete sets of diagonal operators in quantum-statistical mechanics

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

An exact limit for the Peierls distortion energy in an antiferromagnetic chain by means of a renormalization procedure

A renormalization procedure gives a rigorous upper bound for the ground-state energy per spin for a Peierls-distorted antiferromagnetic chain with Heisenberg interaction