PARISI FORMULA FOR THE GROUND STATE ENERGY IN THE MIXED p-SPIN MODEL

被引：26
作者：
Auffinger, Antonio [1 ]
Chen, Wei-Kuo [2 ]
机构：
[1] Northwestern Univ, Dept Math, 2033 Sheridan Rd, Evanston, IL 60208 USA
[2] Univ Minnesota, Dept Math, 127 Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA
来源：
ANNALS OF PROBABILITY | 2017年 / 45卷 / 6B期
基金：
美国国家科学基金会;
关键词：
Spin glasses; ground state energy; Parisi formula;
D O I：
10.1214/16-AOP1173
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
引用
收藏
页码：4617 / 4631
页数：15
相关论文
共 25 条
  • [1] On properties of Parisi measures
    Auffinger, Antonio
    Chen, Wei-Kuo
    [J]. PROBABILITY THEORY AND RELATED FIELDS, 2015, 161 (3-4) : 817 - 850
  • [2] The Parisi Formula has a Unique Minimizer
    Auffinger, Antonio
    Chen, Wei-Kuo
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 335 (03) : 1429 - 1444
  • [3] The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins
    Bovier, Anton
    Klimovsky, Anton
    [J]. ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 : 161 - 241
  • [4] CHEN W. -K., 2016, ENERGY LANDSCAPE MIX
  • [5] CHEN W. - K., 2015, PARISI FORMULA DISOR
  • [6] Crisanti A, 2002, PHYS REV E, V65, DOI 10.1103/PhysRevE.65.046137
  • [7] EXTREMAL CUTS OF SPARSE RANDOM GRAPHS
    Dembo, Amir
    Montanari, Andrea
    Sen, Subhabrata
    [J]. ANNALS OF PROBABILITY, 2017, 45 (02) : 1190 - 1217
  • [8] Broken replica symmetry bounds in the mean field spin glass model
    Guerra, F
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 233 (01) : 1 - 12
  • [9] JAGANNATH A., 2016, LOW TEMPERATURE ASYM
  • [10] A DYNAMIC PROGRAMMING APPROACH TO THE PARISI FUNCTIONAL
    Jagannath, Aukosh
    Tobasco, Ian
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (07) : 3135 - 3150
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