  We propose and study a model for the equilibrium statistical mechanics of a
pressurised semiflexible polymer ring. The Hamiltonian has a term which couples
to the algebraic area of the ring and a term which accounts for bending
(semiflexibility). The model allows for self-intersections. Using a combination
of Monte Carlo simulations, Flory-type scaling theory, mean-field
approximations and lattice enumeration techniques, we obtain a phase diagram in
which collapsed and inflated phases are separated by a continuous transition.
The scaling properties of the averaged area as a function of the number of
units of the ring are derived. For large pressures, the asymptotic behaviour of
the area is calculated for both discrete and lattice versions of the model. For
small pressures, the area is obtained through a mapping onto the quantum
mechanical problem of an electron moving in a magnetic field. The simulation
data agree well with the analytic and mean-field results.
