Shinsuke Nishigaki
Research Subjects
Research Interests
Shinsuke Nishigaki has a total of 9 co-authors. Here are the top co-authors by number of shared publications:
- Chigak Itoi
Department of Physics, GS & CST, Nihon University, Kandasurugadai, Chiyoda, Tokyo 101-8308, Japan
1 shared publication G. Eyal
Department of Physics Technion -Israel Institute of Technology Haifa Israel
1 shared publication- Gernot Akemann
Institut für Theoretische Physik Universität Hannover Appelstraße 2 D-30167 Hannover Germany
1 shared publication - J. Zinn-Justin
CEA-Saclay, Service de Physique Théorique The Niels Bohr Institute Blegdamsvej 17 F-91191 DK-2100 Gif-sur-Yvette Cedex Copenhagen O / FRANCE Denmark
1 shared publication - Moshe Moshe
Department of Physics Technion -Israel Institute of Technology 32000 Haifa Israel
1 shared publication - Norisuke Sakai
Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
1 shared publication
Latest Publications
- Open Access
Renormalization group approach to multiple-arc random matrix models
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.
Open AccessRenormalization group approach to multiple-arc random matrix models
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.
- Open Access
Universality of random matrices in the microscopic limit and the Dirac operator spectrum
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of soft spectrum of the Dirac operator is briefly discussed.
Open AccessUniversality of random matrices in the microscopic limit and the Dirac operator spectrum
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of soft spectrum of the Dirac operator is briefly discussed.
- 1 May 1996
- Published by Elsevier in Physics Letters B
- Vol. 376 (1-3) , 73-81
Wilsonian approximated renormalization group for matrix and vector models in 2 < d < 4
- 1 May 1996
- Published by Elsevier in Physics Letters B
- Vol. 376 (1-3) , 73-81
Wilsonian approximated renormalization group for matrix and vector models in 2 < d < 4
- Open Access
The O(N) vector model in the large N limit revisited: multicritical points and double scaling limit
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the double scaling limit) a massless bound state $O(N)$ singlet is formed and powers of $1/N$ are compensated by IR singularities. The persistence of the $N \to \infty$ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.Open AccessThe O(N) vector model in the large N limit revisited: multicritical points and double scaling limit
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the double scaling limit) a massless bound state $O(N)$ singlet is formed and powers of $1/N$ are compensated by IR singularities. The persistence of the $N \to \infty$ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.