Critical and Multicritical Semi - Random ( 1 + d ) - Dimensional Lattices and Hard Objects in d Dimensions

We investigate models of (1 + d)-D Lorentzian semi-random lattices with one random (space-like) direction and d regular (time-like) ones. We prove a general inversion formula expressing the partition function of these models as the inverse of that of hard objects in d dimensions. This allows for an exact solution of a variety of new models including critical and multicritical generalized (1 + 1)-D Lorentzian surfaces, with fractal dimensions d F = k +1, k = 1, 2, 3, ..., as well as a new model of (1+2)-D critical tetrahedral complexes, with fractal dimension d F = 12/5. Critical exponents and universal scaling functions follow from this solution. We finally establish a general connection between (1 + d)-D Lorentzian lattices and directed-site lattice animals in (1 + d) dimensions.