Polydispersed rods on the square lattice

We study the grand-canonical solution of a system of hard polydispersed rods placed on the square lattice using transfer matrix and finite size scaling calculations. We determine the critical line separating an isotropic from a nematic phase. No second transition to a disordered phase is found at high density, contrary to what is observed in the monodispersed case. The estimates of critical exponents and the central charge on the critical line are consistent with the Ising universality class.