1996/12/26 by S. Higuchi, Saburo Higuchi, Chigak Itoi +5 · 2 citations
Mathematics · Physics and Astronomy · #Critical point (mathematics) #Fixed point #Gaussian #Geometry #Infrared fixed point #Invariant (physics) #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Random Matrices and Applications #Random matrix #Renormalization group #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Unitary state #Universality (dynamical systems) #cond-mat #hep-th
paper · pdf · doi:10.1016/s0370-2693(97)00196-2
published as Phys.Lett. B398 (1997) 123-129 · 11 pages, 1 figure, LaTeX + a4.sty, epsf.sty
arxiv created 1996/12/26 · openalex publication_date 1997/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large-N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjorn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.