Phase Transitions in a Growth-Penalized Partition Model on the Young Lattice

This paper introduces a growth-penalized Gibbs model on integer partitions viewed as nodes of the Young lattice. A general variational framework is developed in which dominant partitions arise as minimizers of an effective free energy functional. Structural results are stated for the existence and identification of finite-size phase transitions, and a computational methodology is described for locating critical parameter values via discrete free-energy crossings.