Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model

J. Bouttier, P. Di Francesco, E. Guitter

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations.

Original languageEnglish (US)
Article number002
Pages (from-to)7411-7440
Number of pages30
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number27
DOIs
StatePublished - Jul 6 2007
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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