O(n)Matrix Spin Model with Unusual Critical Behavior in the Limitn→∞

A generalized $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. It is shown that even for a finite number of spins the model has a phase transition in the limit $n\to \infty$. The transition features a specific-heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also discussed.