Parreira J. R.
Phase Transitions in Hierarchical Models: The Role of Coupling
Coefficients
(14K, LaTeX)
ABSTRACT. We investigate the role of coupling coefficients in determining
the existence of phase transitions in Hierarchical models of Dyson type.
In particular, we show that, when the random spin variables display
discrete symmetry, and the coupling constants are chosen so that
asymptotically they match the behavior of the usual Laplacean, a phase
transition is not expected to occur in two dimensions. We show this fact
in two different ways. First we develop a heuristic argument based on the
balance of energy and entropy in the model. The rigorous proof is then
obtained by the generalization to severl dimensions of a theorem due to
Dyson that states the non-existence of phase transitions when the
coupling constants of the model are bounded.