P-adic numbers and replica symmetry breaking

被引：85

作者：

Parisi, G

Sourlas, N

机构：

[1] Univ Rome La Sapienza, Dipartimento Fis, I-00199 Rome, Italy

[2] Univ Rome La Sapienza, Sez INFN, I-00199 Rome, Italy

[3] Ecole Normale Super, Phys Theor Lab, CNRS, F-75231 Paris, France

来源：

EUROPEAN PHYSICAL JOURNAL B | 2000年 / 14卷 / 03期

关键词：

05.20.-y Classical statistical mechanics; 64.70.Pf Glass transitions; 75.10.Nr Spin-glass and other random models;

D O I：

10.1007/s100510051063

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be a promising tool.

引用

页码：535 / 542

页数：8

共 15 条

[1]

AVETISOV VA, CONDMAT9904360

[2]

CARLUCCI DM, CONDMAT9709200

[3]

CUGLIANDOLO LF, 1993, PHYS REV LETT, V71, P1

[4] GAUSSIAN PROPAGATORS FOR THE ISING SPIN-GLASS BELOW TC [J].

DEDOMINICIS, C ;

KONDOR, I .

JOURNAL DE PHYSIQUE LETTRES, 1985, 46 (22) :1037-1043

[5] Replica Fourier Transforms on ultrametric trees, and block-diagonalizing multi-replica matrices [J].

DeDominicis, C ;

Carlucci, DM ;

Temesvari, T .

JOURNAL DE PHYSIQUE I, 1997, 7 (01) :105-115

[6] THEORY OF SPIN GLASSES [J].

EDWARDS, SF ;

ANDERSON, PW .

JOURNAL OF PHYSICS F-METAL PHYSICS, 1975, 5 (05) :965-974

[7] ULTRAMETRICITY AND ZERO MODES IN THE SHORT-RANGE ISING SPIN-GLASS [J].

KONDOR, I ;

DEDOMINICIS, C .

EUROPHYSICS LETTERS, 1986, 2 (08) :617-624

[8] ON THE P-ADIC 5-POINT FUNCTION [J].

MARINARI, E ;

PARISI, G .

PHYSICS LETTERS B, 1988, 203 (1-2) :52-54

[9] REPLICA SYMMETRY-BREAKING AND THE NATURE OF THE SPIN-GLASS PHASE [J].

MEZARD, M ;

PARISI, G ;

SOURLAS, N ;

TOULOUSE, G ;

VIRASORO, M .

JOURNAL DE PHYSIQUE, 1984, 45 (05) :843-854

[10] MANIFOLDS IN RANDOM-MEDIA - 2 EXTREME CASES [J].

MEZARD, M ;

PARISI, G .

JOURNAL DE PHYSIQUE I, 1992, 2 (12) :2231-2242

← 1 2 →