1992/07/08 by J. Ambjorn, J. AMBJØRN, C. F. Kristjansen +3 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chain (unit) #Field (mathematics) #Genus #Logarithm #Loop (graph theory) #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix model #Physics of Superconductivity and Magnetism #Simple (philosophy) #hep-th
paper · pdf · doi:10.1142/s0217732392002573
published as Mod.Phys.Lett. A7 (1992) 3187-3202 · 17 pages
arxiv created 1992/07/08 · openalex publication_date 1992/11/10 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe an iterative scheme which allows us to calculate any multi-loop correlator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus g contribution to the m-loop correlator depends on a finite number of parameters, namely at most 4g−2+m. We find the generating functional explicitly up to genus three. We show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential.