A large deviation technique is applied to the mean-field ${\phi }^4$ model, providing an exact expression for the configurational entropy $s(v,m)$ as a function of the potential energy $v$ and the magnetization $m$. Although a continuous phase transition occurs at some critical energy $v_c$, the entropy is found to be a real analytic function in both arguments, and it is only the maximization over $m$ which gives rise to a nonanalyticity in $\widehat{s}\left(v\right)={\sup }_{m}s(v,m)$. This mechanism of nonanalyticity-generation by maximization over one variable of a real analytic entropy function is restricted to systems with long-range interactions and has—for continuous phase transitions—the generic occurrence of classical critical exponents as an immediate consequence. Furthermore, this mechanism can provide an explanation why, contradictory to the so-called topological hypothesis, the phase transition in the mean-field ${\phi }^4$ model need not be accompanied by a topology change in the family of constant-energy submanifolds.

• Received 15 July 2005

DOI:https://doi.org/10.1103/PhysRevE.72.056134