  We investigate the phase transition properties of the polymer-Potts model, a
chain composed of monomers with magnetic degrees of freedom, with the
motivation to study the conformation and mark switching dynamics of chromatin.
By the mean-field approximation, we find that the phase transition between the
swollen-disordered state and the compact-ordered state is discrete; it is
first-order as in the long-range Potts model, but with a significantly larger
jump in magnetization (i.e., mark coherence) upon the ordering transition. The
results imply how small changes in epigenetic writer concentrations can lead to
a macroscopic switching of the chromatin state, suggesting a simple mechanism
of discrete switching observed, for instance, in cell differentiation.
