1995/06/29 by Bertrand Eynard, B. Eynard, Charlotte Kristjansen +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Combinatorics #Coupling constant #Eigenvalues and eigenvectors #Exact solutions in general relativity #Genus #Geometry #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Parameter space #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random matrix #Scaling #Scaling limit #Statistical physics #Statistics #Theoretical and Computational Physics #Universality (dynamical systems) #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00469-9
published as Nucl.Phys.B455:577-618,1995 · 44 pages, LaTeX file, no figures
arxiv created 1995/06/29 · openalex publication_date 1995/09/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n∈ ]-2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n=± 2 are treated separately. We give explicit expressions for the genus zero contribution to the one- and two-loop correlators as well as for the genus one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher genera contributions is described. Furthermore we describe how the calculation of the higher genera contributions can be pursued in the scaling limit.