Thermal strings on the lattice and the winding number transition

The partition function of a gas of closed nonoriented strings living on the two-dimensional toroidal lattice is exactly computed. It exhibits a phase transition with the phases differing by the parities of the winding numbers of dominant configurations. Performing the thermodynamic limit first in the 'horizontal' direction the transition is of the first order. Increasing the vertical dimension as well, the latent heat tends to zero and the second-order transition emerges with the characteristic λ-shape of the specific heat. (orig.)