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Álvarez, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2015) Fine structure in the large n limit of the nonhermitian Penner matrix model. Annals of physics, 361 . pp. 440460. ISSN 00034916

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Official URL: http://dx.doi.org/10.1016/j.aop.2015.07.011
URL  URL Type 

http://www.sciencedirect.com/  Publisher 
http://arxiv.org/abs/1507.02386  Organisation 
Abstract
In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large n limit in the nonhermitian Penner matrix model. In these generalizations g_(n)n → t, but the product g_(n)n is not necessarily fixed to the value of the ’t Hooft coupling t. If t > 1 and the limit l = lim_(n→∞) sin(π/g_n) ^(1/n) exists, then the large n limit is welldefined but depends both on t and on l. This result implies that for t > 1 the standard large n limit with g_(n)n = t fixed is not welldefined. The parameter l determines a fine structure of the asymptotic eigenvalue support: for l ≠ 0 the support consists of an interval on the real axis with charge fraction Q = 1 − 1/t and an ldependent oval around the origin with charge fraction 1/t. For l = 1 these two components meet, and for l = 0 the oval collapses to the origin. We also calculate the total electrostatic energy Ԑ which turns out to be independent of l, and the free energy Ƒ = Ԑ  Ǫ ln l, which does depend of the fine structure parameter l. The existence of large n asymptotic expansions of Ƒ beyond the planar limit as well as the doublescaling limit are also discussed.
Item Type:  Article 

Additional Information:  © Academic Press Inc Elsevier Science. 
Uncontrolled Keywords:  Laguerrepolynomials; Jacobipolynomials; Moduli space; Parameters; Asymptotics; Behavior 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  33245 
Deposited On:  24 Sep 2015 16:46 
Last Modified:  10 Dec 2018 15:09 
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