Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries Original Research Article

An analytic method of calculating conformal partition functions of solvable lattice models is presented. Our technique involves the solution of transfer matrix functional equations in the scaling limit, and unifies the work of Albertini et al. on the classification of transfer matrix eigenvalues with that of Khimper and Pearce on finite-size corrections. As an illustration, conformal partition functions of the tricritical hard square model with fixed boundaries are derived. The resulting Virasoro characters arise in their fermionic representation and agree with the Coulomb gas calculations of Saleur and Bauer.