ANALYTIC CALCULATION OF SCALING DIMENSIONS - TRICRITICAL HARD SQUARES AND CRITICAL HARD HEXAGONS

The finite-size corrections, central charges c, and scaling dimensions x of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the communting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtain c = 7/10, x = 3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtain c = 4/5, x = 2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.