Showing papers on "Partition function (quantum field theory) published in 1983"

A Langevin approach to fermion and quantum spin correlation functions

Abstract: By using spin-coherent states, the author shows that correlation functions for fermions or quantum spins follow from solutions to Langevin equations associated with a functional integral representation of the partition function. His method is applicable to any number of dimensions, may also be combined with boson variables, and is suitable for computer simulations.

A cluster theory for electrolytes

Abstract: A simple extension of the Bjerrum theory is formulated and examined. Clusters of trimers as well as dimers are included. The intercluster partition function is evaluated in the mean spherical approximation. At low concentrations this cluster theory gives good results for the thermodynamic functions and for the radial distribution function for unlike pairs. The radial distribution function for like pairs is less satisfactory. The theory is less successful at higher concentrations but is always at least as good as the mean spherical approximation.

On the Operator Formulation of the Polyatomic Molecule Partition Function

Abstract: Abstract The Nielsen Hamiltonian of the general polyatomic molecule including anharmonicity and its resonances, Coriolis-coupling and its resonances, and rotation-vibration interaction are treated by statistical perturbation theory in its operator form. By generating function methods and operator theorems, which are treated in an appendix, cumbersome calculations with non-commuting operators are avoided. The results for H2O and SO2 agree very well with accurate numerical calculations from the literature. Qualitative conclusions on the convergence of the perturbation series are drawn from the numerical calculations for model systems.

Study of a two-dimensional fully frustrated model

Abstract: The authors consider a fully frustrated Ising model on a square lattice, depending on four parameters. The partition function is shown to be equivalent to the two-parameter (ferromagnetic) Onsager partition function. This result generalises a relation established by Southern et al. (1980), and can be checked in the particular case of the (one-parameter) Villain model. In particular, the residual entropy of the Villain model is linked to the free energy of the Onsager model at criticality. The reduction from four to two parameters, occurring in this mapping, is studied in the light of the inverse relation satisfied by the partition function of the frustrated model.

Zeros of the partition function using theorems of Ruelle

Abstract: Theorems of Ruelle which provide a technique for finding regions of the relevant complex planes free of zeros of the partition function are used to study certain Ising spin systems. Of particular interest is the antiferromagnetic triangle lattice system with h≠0 and systems having three-body interactions.

Partition function of a particle subject to Gaussian noise

Abstract: We study the averaged partition function for a quantum particle subjected to Gaussian noise using the path integral representation. The noise is characterized by a covariance function with a strength and a range. It falls off rapidly with distance but the analytic form at short distances and the dimensionality are important. The remaining parameter is the thermal length of the particle. For a finite range we study the behavior of the partition function over the entire domain of strengths and thermal lengths. The techniques used are successively more accurate upper and lower bounds that include contributions from configurations involving traps. Particular attention is paid to a self-consistent field analysis lower bound and to a nonlocal quadratic action bound. We also study the white noise limit, i.e., vanishing range with finite values of the other parameters. In one dimension the white noise limit leads to convergent results. In three or higher dimensions the divergent terms can be isolated and computed. In two dimensions the degree of divergences changes at a finite value of the product of the strength and thermal length squared.

Generating functional models for a statistical system near a phase transition

Abstract: Starting from an assumed form of the distribution function near the phase transition point, an expression for the generating functional of a statistical system suitable for describing two-phase states of matter is derived We then obtain formulas for the partition function and correlation functions by the standard procedure