Infinite heat capacity anomaly for two-level systems with a mean-field coupling.

This paper examines the statistical mechanics of collections of two-level systems that experience a nonlinear mean-field coupling. The coupling reduces the two-level excitation energy by an amount that depends on the number of excitations already present; in other words the energy spectrum manifests a cooperative "softening" phenomenon. An exact solution in the infinite system limit is presented for key aspects of a specific case, the "logarithmic" model. This model exhibits a symmetric infinite heat capacity anomaly with divergence exponent equal to 2/3. Furthermore the divergence evolves from maxima with heights asymptotically proportional to N(1/2) as the number of coupled two-level systems increases to infinity.