Showing papers on "Partition function (quantum field theory) published in 1975"

Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics

Abstract: We show, by making use of the functional integral technique, that, for a large class of useful quantum statistical systems, the partition function is, with respect to the coupling constant, the Laplace transform of a positive measure. As a consequence, we derive an infinite set of monotonicly converging upper and lower bounds to it. In particular, the lowest approximation appears to be identical to the Gibbs–Bogolioubov variational bound, while the next approximations, for which we give explicit formulas for the first few ones, lead to improve the previous bound. The monotonic character of the variational successive approximations allows a new approach towards the thermodynamical limit.

Volume dependence of Schwinger functions in the Yukawa2 quantum field theory

Abstract: We prove upper bounds on the partition function and Schwinger functions for the Euclidean Yukawa2 quantum field theory which depend on the interaction volume Λ only through a term of the form (const)|Λ|. We also prove a lower bound of the form (const)|λ| for the partition function. We work throughout in the Matthews-Salam representation with the fermions integrated out.

Cayley tree approximation for the Potts model

Abstract: An approximation to the partition function of the standard Potts model is constructed by considering only the dominant tree-like configurations. This approximation gives a good representation of the positions of the non-physical singularities obtained from low-temperature series, and it is also possible to relate the behaviour of the approximations to the order of the Potts model transitions. It is found that for the two-dimensional lattices studied the transition is first-order for q>4, whereas for the three-dimensional lattices it is first-order when q>2.

On Falicov's model for metal-insulator-transitions

Abstract: It is shown that for a certain class of band structures the first order metal-to-insulator phase transition predicted by Falicov's model falls in a region of parameters, where the system has excitonic states. The influence of these states on the phase transition is discussed by working directly from the partition function of the system.

Functional Integral Representations of Partition Function Without Limiting Procedure. Techniques of Calculation of Moments

Abstract: A definition of the Feynman path integral which does not rest on a limiting procedure based on time-slicing has been given by DeWitt-Morette. We present in this paper a discussion of real Gaussian measures and formulate expressions for the quantum statistical partition function directly in terms of measures of integration on the topological vector space o0 of continuous functions defined on the time intervalT = (ta,tb), such thatx(ta,tb)=0 for allx ɛ o0. We give a definition of a measure for the space o0 equivalent to the path integral based on the Uhlenbeck-Ornstein probability distribution. We give expressions for the partition function using the Wiener-Feynman measure and the Uhlenbeck-Ornstein measure. As an exercise in the use of the new techniques, we present calculations of moments of potential functions. The techniques will enable one to solve in a rigorous manner practical problems in quantum statistical mechanics.

Phase transition phenomena and the Lippmann—Schwinger variational principle

Abstract: It is shown that the partition function need not be determined uniquely if a generalized matrix eigenvalue equation of the type (W1−PW2)Y=0 possesses a nontrivial solutionY. The solution may be physically relevant if the parameterP is real. We derive the above eigenvalue equation and discuss its solution. In this context some basic asymptotic considerations are summarized in a theorem.