G. Vertogen

MOLECULAR BIAXIALITY AND TEMPERATURE-DEPENDENCE OF CHOLESTERIC PITCH

Abstract An interaction between chiral molecules is proposed in terms of the orientations of their molecular principal axes. An expression is given for the pitch depending on the order parameters P 2 = 3 2 cos 2 θ − 1 2 and D = 3 2 sin 2 θ cos 2ψ and molecular properties.

The dicke maser model

Abstract A simple method is presented to calculate the thermodynamic properties of the Dicke maser model.

On the thermodynamic equivalence of Van Der Waals spin systems

Abstract It is shown that solving a Van der Waals spin system is equivalent to solving some Van der Waals Ising system of the same spin variable in the thermodynamic limit in the case that the state of the system is homogeneous.

COEXISTENCE OF FERROMAGNETISM AND SUPERCONDUCTIVITY IN A SUPERCONDUCTING ALLOY

Abstract A model for a superconducting alloy doped with magnetic impurities is solved exactly. The model consists of a combination of the BCS model and the Zener s-d exchange-interaction model. Its behaviour appears to be strongly dependent on the impurity concentration and the coupling parameters belonging to the BCS model and the s-d exchange-interaction model. At very low temperatures the system is always a ferromagnet or a superconductor. Coexistence of superconductivity and ferromagnetism is only possible at finite temperatures for certain values of the coupling parameters and the concentration of magnetic impurities. The transitions from the mixed state to the superconducting and to the magnetic state do not need to be continuous, i.e., second order.

EXACT SOLUTION OF ZENERS S-D EXCHANGE INTERACTION MODEL

Abstract The exact solution for the Zener s-d exchange-interaction model is presented. The system exhibits a second-order phase transition. It appears that the critical temperature T c is independent of the sign of the s-d exchange interaction. Under the assumption that the conduction band has a constant density of states, an explicit expression for T c is derived in terms of the conduction-band width D , the concentration c of the magnetic impurity spins and the strength J of the s-d exchange coupling. For the case of an antiferromagnetic exchange coupling it is found that the directions of the magnetization of the conduction electrons and of the impurity spins depend on the magnetic field strength.

The Ising problem

A method to solve Ising problems is developed giving all correlation functions. As an example the one-dimensional nearest and next-nearest neighbour models have been calculated explicitly.

On the indirect exchange interaction in terms of an exactly soluble model

Abstract An exactly soluble model is formulated for the case of two localized magnetic moments with spin S = 1 2 in ferro- or antiferromagnetic s-f ors-d interaction with a conduction-electron gas. This indirect exchange interaction model shows important differences between a ferro- and antiferromagnetic s-f interaction, e.g. in case of an antiferromagnetic s-f interaction both magnetic moments are never coupled in a purely ferromagnetic way. The model also exhibits the feature that in case the distance between both moments satisfies a special condition the correlation between these moments disappears, i.e. the indirect exchange interaction equals zero for these distances.

Absence of magnetic phase transition in one- and two-dimensional s-d interaction models

Abstract By means of the Bogoliubov inequality it is proved that the s-d interaction between conduction electrons and localized magnetic moments does not give rise to a spontaneous magnetic ordering in one- or two-dimensional systems at finite temperatures.

COEXISTENCE OF SUPERCONDUCTIVITY AND MAGNETISM

Abstract A model consisting of the B.C.S.-Hamiltonian and Zeners s-d exchange interaction is solved rigorously in the thermodynamic limit. Coexistence of superconductivity and magnetism is only possible for an impurity spin concentration smaller than a half at T ≠ 0.

Numerical results in the Kondo problem

Abstract A numerically solvable Kondo model is formulated. It is shown that for certain cases the limit T → 0 does not yield the correct ground state.