ANALYTIC SOLUTION OF THE RANDOM ISING-MODEL IN ONE-DIMENSION

被引：8

作者：

PALADIN, G ^{[1
]}

SERVA, M ^{[1
]}

机构：

[1] UNIV AQUILA,DIPARTIMENTO MAT,I-67100 COPPITO AQUILA,ITALY

来源：

PHYSICAL REVIEW LETTERS | 1992年 / 69卷 / 05期

关键词：

D O I：

10.1103/PhysRevLett.69.706

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An analytic expression is derived for the Lyapunov exponents of the product of random transfer matrices related to the Ising model with quenched disorder in one dimension. We find a deterministic map which transforms the original system into a new one with zero external field and constant coupling. The free energy and the rate of correlation decay are thus obtained in terms of an exponentially convergent series. Our results can be generalized to the product of random matrices with nonzero entries.

引用

页码：706 / 709

页数：4

共 9 条

[1] THE STABILITY OF LARGE RANDOM MATRICES AND THEIR PRODUCTS [J].

COHEN, JE ;

NEWMAN, CM .

ANNALS OF PROBABILITY, 1984, 12 (02) :283-310

[2] LYAPUNOV EXPONENTS OF LARGE, SPARSE RANDOM MATRICES AND THE PROBLEM OF DIRECTED POLYMERS WITH COMPLEX RANDOM WEIGHTS [J].

COOK, J ;

DERRIDA, B .

JOURNAL OF STATISTICAL PHYSICS, 1990, 61 (5-6) :961-986

[3]

CRISANTI A, IN PRESS SERIES SOLI

[4] PRODUCT OF RANDOM MATRICES IN A MICROCANONICAL ENSEMBLE [J].

DEUTSCH, JM ;

PALADIN, G .

PHYSICAL REVIEW LETTERS, 1989, 62 (07) :695-699

[5] MEAN-FIELD THEORY OF THE 3-DIMENSIONAL ANISOTROPIC ISING-MODEL AS A 4-DIMENSIONAL MAPPING [J].

JENSEN, MH ;

BAK, P .

PHYSICAL REVIEW B, 1983, 27 (11) :6853-6868

[6]

MAINIERI R, 1992, PHYS REV LETT, V68, P1962

[7]

Oseledets V. I., 1968, T MOSK MAT OBSHCHEST, V19, P179

[8]

PALADIN G, UNPUB

[9]

[No title captured]

← 1 →