Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that (beyond a critical value of a coupling) the spin system considered acquires a first order transition as a result of the field dependence of its effective mass, whereas models with constant mass exhibit only second order transitions.Comment: 10 pages, 3 figure

A criterion is derived for the determination of parameter domains of first order phase transitions in quantum mechanical tunneling models. The criterion is tested by application to various models, in particular to some which have been used recently to explore spin tunneling in macroscopic particles. In each case agreement is found with previously heuristically determined domains. *

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first-or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.

The point-particle-like Hamiltonian of a biaxial spin particle with external magnetic field along the hard axis is obtained in terms of the potential field description of spin systems with exact spin-coordinate correspondence. The Zeeman energy term turns out to be an effective gauge potential which leads to a nonintegrable phase of the Euclidean Feynman propagator. The phase interference between clockwise and anticlockwise under barrier propagations is recognized explicitly as the Aharonov-Bohm effect. An additional phase which is significant for quantum phase interference is discovered with the quantum theory of spin systems besides the known phase obtained with the semiclassical treatment of spin. We also show the energy dependence of the * e-mail:jqliang@mail.sxu.edu.cn † e-mail: mueller1@pysik.uni-kl.de ‡ e-mail:dkpark@genphys.kyungnam.ac.kr 1 effect and obtain the tunneling splitting at excited states with the help of periodic instantons.