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

P. Di Francesco, E. Guitter

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)897-927
Number of pages31
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number4
DOIs
StatePublished - Feb 1 2002
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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