Rigorous solution of the Gardner problem

被引：31

作者：

Shcherbina, M

Tirozzi, B

机构：

[1] Ukrainian Acad Sci, Inst Low Temp Phys, UA-310108 Kharkov, Ukraine

[2] Univ Roma La Sapienza, Dept Phys, I-00185 Rome, Italy

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2003年 / 234卷 / 03期

关键词：

D O I：

10.1007/s00220-002-0783-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of p random patterns. The Gardner formula for this volume in the limit N, p --> infinity, p/N --> alpha is proven for all values of alpha. Besides, we prove a useful criterion for the factorisation of all correlation functions for a class of models of classical statistical mechanics.

引用

页码：383 / 422

页数：40

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