Temperature dependence of free energy and entropy in arithmetic Ising models

Determine how the free energy and entropy change as functions of temperature in arithmetic Ising models that realize entropic order, in order to verify enhanced entropy in their ordered phases.

Background

The paper studies arithmetic Ising models as minimal models exhibiting entropic order, in which an ordered phase can be favored at higher temperatures because of enhanced entropy. The authors explain that understanding this phenomenon requires determining the temperature dependence of thermodynamic quantities, especially the free energy and entropy. Although the paper computes these quantities exactly for the model considered, the stated unresolved issue concerns their behavior as functions of temperature in entropic-order models more generally.