Flexibility of the Pressure Function

We study the flexibility of pressure function a continuous potential (observable) with respect to parameter regarded as inverse temperature. The points non-differentiability this are particular interest in statistical physics, since they correspond phase transitions. It is well known that convex, Lipschitz, and has an asymptote at infinity. prove setting one-dimensional compact symbolic systems these only restrictions. present method explicitly construct whose coincides any prescribed convex Lipschitz asymptotically linear starting given positive value parameter. In fact, we establish multidimensional version result. As consequence, obtain for observable transitions can occur countable dense set temperature values. go further show one vary cardinality ergodic equilibrium states be number, finite or infinite.