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

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

2001-04-20

arxiv.org/abs/cond-mat/0104383v2

J.Phys.A35:897-928,2002

Physics

Condensed Matter

Statistical Mechanics

44 pages, 15 figures, tex, harvmac, epsf, references added

Scientific paper

10.1088/0305-4470/35/4/304

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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