کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856047 | 1529850 | 2015 | 21 صفحه PDF | دانلود رایگان |
In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large nn limit in the non-Hermitian Penner matrix model. In these generalizations gnn→tgnn→t, but the product gnngnn is not necessarily fixed to the value of the ’t Hooft coupling tt. If t>1t>1 and the limit l=limn→∞|sin(π/gn)|1/nl=limn→∞|sin(π/gn)|1/n exists, then the large nn limit is well-defined but depends both on tt and on ll. This result implies that for t>1t>1 the standard large nn limit with gnn=tgnn=t fixed is not well-defined. The parameter ll determines a fine structure of the asymptotic eigenvalue support: for l≠0l≠0 the support consists of an interval on the real axis with charge fraction Q=1−1/tQ=1−1/t and an ll-dependent oval around the origin with charge fraction 1/t1/t. For l=1l=1 these two components meet, and for l=0l=0 the oval collapses to the origin. We also calculate the total electrostatic energy EE, which turns out to be independent of ll, and the free energy F=E−Qlnl, which does depend on the fine structure parameter ll. The existence of large nn asymptotic expansions of FF beyond the planar limit as well as the double-scaling limit are also discussed.
Journal: Annals of Physics - Volume 361, October 2015, Pages 440–460