2001/04/30 by Philippe Di Francesco, Emmanuel Guitter · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech #hep-th #math.CO
paper · pdf · doi:10.1088/0305-4470/35/4/304
published as J.Phys.A35:897-928,2002 · 44 pages, 15 figures, tex, harvmac, epsf, references added
arxiv created 2001/05/04 · openalex publication_date 2002/01/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.