查看“︁楊李定理”︁的源代码

在[[统计力学]]和[[统计场论|統計場論]]中，'''楊李定理（'''或'''杨李单位圆定理）'''說：有些[[铁磁性|铁磁]][[配分函數]]的零點都是[[虚数]]。該定理是以[[楊振寧]]和[[李政道]]命名的。【{{Harvard citations|txt|first1=T. D.|last1=Lee|first2=C. N.|last2=Yang|year=1952}}、{{Harvard citation|Lee|Yang|1952}}】

== 應用 ==

* [[易辛模型|伊辛型]]
*[[海森堡模型]]，Asano contractions<ref>{{Cite journal|title=Lee-Yang Theorem and the Griffiths Inequality for the Anisotropic Heisenberg Ferromagnet|url=https://link.aps.org/doi/10.1103/PhysRevLett.24.1409|last=Asano|first=Taro|date=1970-06-22|journal=Physical Review Letters|issue=25|doi=10.1103/PhysRevLett.24.1409|volume=24|pages=1409–1411}}</ref><ref>{{Cite journal|title=Generalization of the Lee-Yang Theorem|url=https://academic.oup.com/ptp/article/40/6/1328/1871804|last=Asano|first=Taro|date=1968-12-01|journal=Progress of Theoretical Physics|issue=6|doi=10.1143/PTP.40.1328|volume=40|pages=1328–1336|language=en|issn=0033-068X|access-date=2020-03-07|archive-date=2020-06-23|archive-url=https://web.archive.org/web/20200623082718/https://academic.oup.com/ptp/article/40/6/1328/1871804|dead-url=no}}</ref>
* {{Harvard citation text|Simon|Griffiths|1973}} 
* {{Harvard citation text|Newman|1974}} 
* {{Harvard citation text|Lieb|Sokal|1981}}
*[[黎曼猜想]]、[[黎曼ζ函數]]、[[动力系统]]<ref>{{Cite journal|title=NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS|url=https://www.worldscientific.com/doi/abs/10.1142/S0129055X99000325|last=Knauf|first=Andreas|date=1999-09|journal=Reviews in Mathematical Physics|issue=08|doi=10.1142/S0129055X99000325|volume=11|pages=1027–1060|language=en|issn=0129-055X|access-date=2020-03-07|archive-date=2021-04-19|archive-url=https://web.archive.org/web/20210419072400/https://www.worldscientific.com/doi/abs/10.1142/S0129055X99000325|dead-url=no}}</ref>

== 數學定理 ==
[[哈密爾頓]]{{dn|date=2024年08月10日}}是

: <math>H = -\sum J_{jk}S_jS_k-\sum z_jS_j</math>

若<math>S_j S_k \ge 0</math>，則H是[[鐵磁性]]的。

[[配分函数]]是

: <math>Z = \int e^{- H} d\mu_1(S_1)\cdots d\mu_N(S_N)</math>

: <math> \int e^{b S^2} d|\mu_j(S)| < \infty, \, \forall b \in \mathbb{R}.</math>

: <math> \int e^{h S} d\mu_j(S) \neq 0, \, \forall h \in \mathbb{H}_{+}:=\{ z \in \mathbb{C} | \Re{z}>0 \} </math>

'''楊李定理'''說

: <math> Z(\{ z_j \}) \neq 0, \, \forall z_j \in \mathbb{H}_{+}</math>

== 参考文献 ==
{{Reflist}}

== 阅读 ==

* {{Citation|last=Itzykson|first=Claude|last2=Drouffe|first2=Jean-Michel|title=Statistical field theory. Vol. 1|publisher=[[Cambridge University Press]]|series=Cambridge Monographs on Mathematical Physics|isbn=978-0-521-34058-8|mr=1175176|year=1989}}
*{{Citation | last1=Knauf | first1=Andreas | title=Number theory, dynamical systems and statistical mechanics |mr=1714352 | year=1999 | journal=Reviews in Mathematical Physics | issn=0129-055X | volume=11 | issue=8 | pages=1027–1060|doi=10.1142/S0129055X99000325| bibcode=1999RvMaP..11.1027K | citeseerx=10.1.1.184.8685 }}
* {{Citation|last=Lee|first=T. D.|last2=Yang|first2=C. N.|title=Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model|doi=10.1103/PhysRev.87.410|year=1952|journal=[[Physical Review]]|issn=0031-9007|volume=87|number=3|pages=410–419}}
* {{Citation|doi=10.1007/BF01213009|last=Lieb|first=Elliott H.|last2=Sokal|first2=Alan D.|title=A general Lee-Yang theorem for one-component and multicomponent ferromagnets|mr=623156|year=1981|journal=Communications in Mathematical Physics|issn=0010-3616|volume=80|number=2|pages=153–179|url=http://projecteuclid.org/euclid.cmp/1103919874|accessdate=2020-03-07|archive-date=2020-07-17|archive-url=https://web.archive.org/web/20200717225454/https://projecteuclid.org/euclid.cmp/1103919874|dead-url=no}}
* {{Citation|last=Newman|first=Charles M.|title=Zeros of the partition function for generalized Ising systems|doi=10.1002/cpa.3160270203|mr=0484184|year=1974|journal=[[Communications on Pure and Applied Mathematics]]|issn=0010-3640|volume=27|number=2|pages=143–159}}
*{{Citation | doi=10.1007/BF01645626 | last1=Simon | first1=Barry | author1-link=Barry Simon | last2=Griffiths | first2=Robert B. | title=The (φ<sup>4</sup>)<sub>2</sub> field theory as a classical Ising model | url=http://projecteuclid.org/euclid.cmp/1103859251 | mr=0428998 | year=1973 | journal=Communications in Mathematical Physics | issn=0010-3616 | volume=33 | issue=2 | pages=145–164 | bibcode=1973CMaPh..33..145S | citeseerx=10.1.1.210.9639 | s2cid=123201243 | accessdate=2020-03-07 | archive-date=2020-06-10 | archive-url=https://web.archive.org/web/20200610203249/https://projecteuclid.org/euclid.cmp/1103859251 | dead-url=no }}
* {{Citation|last=Yang|first=C. N.|last2=Lee|first2=T. D.|title=Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation|doi=10.1103/PhysRev.87.404|year=1952|journal=[[Physical Review]]|issn=0031-9007|volume=87|number=3|pages=404–409}}

[[Category:杨振宁]]
[[Category:李政道]]
[[Category:量子場論]]
[[Category:統計場論]]
[[Category:統計力學]]