THE LOGARITHMIC SOBOLEV INEQUALITY FOR DISCRETE SPIN SYSTEMS ON A LATTICE

被引：122

作者：

STROOCK, DW ^{[1
]}

ZEGARLINSKI, B ^{[1
]}

机构：

[1] RUHR UNIV BOCHUM,FAK MATH,W-4630 BOCHUM 1,GERMANY

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1992年 / 149卷 / 01期

关键词：

D O I：

10.1007/BF02096629

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

For finite range lattice gases with a finite spin space, it is shown that the Dobrushin-Shlosman mixing condition is equivalent to the existence of a logarithmic Sobolev inequality for the associated (unique) Gibbs state. In addition, implications of these considerations for the ergodic properties of the corresponding Glauber dynamics are examined.

引用

页码：175 / 193

页数：19

共 16 条

[1]

Aizenman Michael, 1987, PERCOLATION THEORY E, P1

[2]

Deuschel J. D., 1989, PURE APPL MATH SERIE, V137

[3]

Dobrushin R. L., 1985, Statistical Physics and Dynamical Systems: Rigorous Results, P371

[4]

Dobrushin R. L., 1985, Statistical Physics and Dynamical Systems: Rigorous Results, P347