THE REPLICA-SYMMETRICAL SOLUTION WITHOUT REPLICA TRICK FOR THE HOPFIELD MODEL

被引:38
作者
PASTUR, L [1 ]
SHCHERBINA, M [1 ]
TIROZZI, B [1 ]
机构
[1] UNIV ROME,DEPT MATH,I-00185 ROME,ITALY
关键词
REPLICA SYMMETRY; SELF-AVERAGENESS; SADDLE-POINT EQUATIONS;
D O I
10.1007/BF02188221
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We derive the saddle-point equations for the order parameters of the Hopfield model in the case of replica symmetry without using the replica trick, but assuming that the Edwards-Anderson parameter is a self-averaging quantity.
引用
收藏
页码:1161 / 1183
页数:23
相关论文
共 17 条
[1]  
Amit D. J, 1989, MODELLING BRAIN FUNC
[2]   STATISTICAL-MECHANICS OF NEURAL NETWORKS NEAR SATURATION [J].
AMIT, DJ ;
GUTFREUND, H ;
SOMPOLINSKY, H .
ANNALS OF PHYSICS, 1987, 173 (01) :30-67
[3]  
GRENSING P, 1987, J PHYS A, V20, P2935
[4]   NEURONS WITH GRADED RESPONSE HAVE COLLECTIVE COMPUTATIONAL PROPERTIES LIKE THOSE OF 2-STATE NEURONS [J].
HOPFIELD, JJ .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1984, 81 (10) :3088-3092
[5]   NEURAL NETWORKS AND PHYSICAL SYSTEMS WITH EMERGENT COLLECTIVE COMPUTATIONAL ABILITIES [J].
HOPFIELD, JJ .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1982, 79 (08) :2554-2558
[6]  
LITTLE WA, 1974, MATH BIOSCI, V13, P13101
[7]  
LITTLE WA, 1974, MATH BIOSCI, V39, P13281
[8]   EXACTLY SOLUBLE SPIN-GLASS MODEL [J].
LUTTINGER, JM .
PHYSICAL REVIEW LETTERS, 1976, 37 (12) :778-782
[9]  
Mezard M., 1987, SPIN GLASS THEORY IN, V9
[10]  
Pastur L. A., 1978, TEORET MAT FIZ, V35, P193