Publication : t01/042

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 $d_F=k+1$, $k=1,2,3,...$, 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.

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