THE ONSAGER FORMULA, THE FISHER-HARTWIG CONJECTURE, AND THEIR INFLUENCE ON RESEARCH INTO TOEPLITZ-OPERATORS

被引：19

作者：

BOTTCHER, A

机构：

[1] Fachbereich Mathematik, TU Chemnitz-Zwickau, Chemnitz, D-09009

来源：

JOURNAL OF STATISTICAL PHYSICS | 1995年 / 78卷 / 1-2期

关键词：

ISING MODEL; CORRELATION FUNCTIONS; SPONTANEOUS MAGNETIZATION; TOEPLITZ DETERMINANTS; SZEGO LIMIT THEOREMS; TOEPLITZ OPERATORS;

D O I：

10.1007/BF02183366

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This is not primarily a paper about applications of mathematics to statistical physics, but rather a report on how a particular problem of statistical physics has resulted in an extensive mathematical theory. The problem alluded to is the computation of the spontaneous magnetization M(o)(T) of the two-dimensional Ising model with nearest-neighbor interactions, whose solution for temperatures T below the Curie point T-C was given by the famous formula of Lars Onsager in 1948. The theory grown out of this formula is the edifice of Toeplitz determinants, matrices, and operators.

引用

页码：575 / 584

页数：10

共 21 条

[11]

Fisher M E, 1968, ADV CHEM PHYS, V15, P333, DOI DOI 10.1002/9780470143605.CH18

[12] TOEPLITZ MATRICES, TRANSLATION KERNELS AND A RELATED PROBLEM IN PROBABILITY THEORY [J].