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