Fluctuations of the Free Energy of the Spherical Sherrington-Kirkpatrick Model

被引：45

作者：

Baik, Jinho ^{[1
]}

Lee, Ji Oon ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea

来源：

JOURNAL OF STATISTICAL PHYSICS | 2016年 / 165卷 / 02期

基金：

美国国家科学基金会;

关键词：

Free energy; Spherical SK model; Tracy-Widom distribution; LOCAL EIGENVALUE STATISTICS; LINEAR SPECTRAL STATISTICS; DIRECTED POLYMERS; RANDOM MATRICES; UNIVERSALITY; ASYMPTOTICS; EDGE; CLT; POLYNOMIALS; UNITARY;

D O I：

10.1007/s10955-016-1610-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the fluctuations of the free energy for the 2-spin spherical Sherrington-Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy-Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.

引用

页码：185 / 224

页数：40

共 57 条

[1] SOME RIGOROUS RESULTS ON THE SHERRINGTON-KIRKPATRICK SPIN-GLASS MODEL [J].