The Feynman–Kac theorem and Bogolyubov inequality are applied to obtain a lower bound and an upper bound to the free energy of the s–d Hamiltonian with locally smeared interactions between electrons and impurities. The two bounds, which express in terms of the free energy of impurities in a...

The divergence of the perturbation series in quantum field theory is reviewed and an argument presented showing that, at least in the unrenormalised theory, it must be asymptotic in the Poincaré sense. Some basic concepts of asymptotic series are reviewed. By combining momentum analyticity with...

The equilibrium state of a triangular pile of particles, interconnected by linear springs and subjected to the force of gravity, is explored algebraically. A subset of the springs is treated as weak in relation to the others and perturbation theory is used to obtain the zero order and first...

Analytic, explicit and non-empirical equations of state for the double Yukawa and hard core double Yukawa fluids are presented. They are based on a second-order inverse temperature expansion of the free energy within the mean spherical approximation. These equations of state yield good results...

A simple expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid is used in combination with Barker–Henderson perturbation theory to obtain the thermodynamic properties of triangular-well fluids. These properties are expressed...

The RKKY perturbation scheme for the spin 12 s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a...

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The series for the exact moments, if not the distribution...