Nonhermitian random matrix models
Abstract
We introduce an extension of the diagrammatic rules in random matrix theory and apply it to nonhermitian random matrix models using the 1/ N approximation. A number of oneand twopoint functions are evaluated on their holomorphic and nonholomorphic supports to leading order in 1/ N. The onepoint functions describe the distribution of eigenvalues, while the twopoint functions characterize their macroscopic cotrelations. The generic form for the twopoint functions is obtained, generalizing the concept of macroscopic universality to nonhermitian random matrices. We show that the holomorphic and nonholomorphic one and twopoint functions condition the behavior of pertinent partition functions to order O(1/ N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)004185
 arXiv:
 arXiv:condmat/9612240
 Bibcode:
 1997NuPhB.501..603J
 Keywords:

 Condensed Matter;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 49 pages RevTex, with modified feynmf sty, 9 EPSF figures included. Version submitted to Nuclear Physics B