96-679 Parreira J. R.

Phase Transitions in Hierarchical Models: The Role of Coupling Coefficients (14K, LaTeX) Dec 18, 96

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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.

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