Dr DA Lavis
Department of Mathematics
Room 22DM/B, Strand Building
Since my formal retirement my main area of interest has moved towards the foundations of statistical mechanics. In particular I am interested in exploring the nature of irreversibility and equilibrium. In the first of two recent papers I have reexamined the role played by the spin-echo system in discussions of these questions. In the second I have argued that, in order to reconcile the Boltzmann and Gibbs approaches to statistical mechanics, it is necessary to abandon the binary property of being or not being in equilibrium in favour of a continuous property which I call 'commonness'.
In the past series expansion methods have been used with one expansion parameter and numerical coefficients to obtain critical properties at one point in phase space. The object of my research with B. W. Southern of the University of Manitoba is to provide the beginning of a general methodology for using series to explore the whole of the phase space. We are using the finite-lattice method to develop series where the coefficients are polynomial functions of the Boltzmann factors for a number of other couplings. We are currently investigating a modified three-state Potts model on a triangular lattice with a chiral term around each triangle. This chiral term is of particular interest as it forms the basis for the development of lattice models with directional bonding. These have been used to simulate water-like behaviour.
I am currently preparing, for Springer, a revised one-volume edition of the two books on the Statistical mechanics of Lattice Systems, which I published in 1999 in collaboration with G. M. Bell.