Critical and multicritical semi-random (1 +d)-dimensional lattices and hard objects inddimensions

Abstract

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 dF = k + 1, k = 1,2,3,... , as well as a new model of (1+2)D critical tetrahedral complexes, with fractal dimension dF = 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.