楊李定理
在統計力學和統計場論中,楊李定理(或楊李單位圓定理)說:有些鐵磁配分函數的零點都是虛數。該定理是以楊振寧和李政道命名的。【T. D. Lee and C. N. Yang (1952)、(Lee & Yang 1952)】
應用
- 伊辛型
- 海森堡模型,Asano contractions[1][2]
- Simon & Griffiths (1973)
- Newman (1974)
- Lieb & Sokal (1981)
- 黎曼猜想、黎曼ζ函數、動力系統[3]
數學定理
若,則H是鐵磁性的。
配分函數是
楊李定理說
參考文獻
- ^ Asano, Taro. Lee-Yang Theorem and the Griffiths Inequality for the Anisotropic Heisenberg Ferromagnet. Physical Review Letters. 1970-06-22, 24 (25): 1409–1411. doi:10.1103/PhysRevLett.24.1409.
- ^ Asano, Taro. Generalization of the Lee-Yang Theorem. Progress of Theoretical Physics. 1968-12-01, 40 (6): 1328–1336 [2020-03-07]. ISSN 0033-068X. doi:10.1143/PTP.40.1328. (原始內容存檔於2020-06-23) (英語).
- ^ Knauf, Andreas. NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS. Reviews in Mathematical Physics. 1999-09, 11 (08): 1027–1060 [2020-03-07]. ISSN 0129-055X. doi:10.1142/S0129055X99000325. (原始內容存檔於2021-04-19) (英語).
閱讀
- Itzykson, Claude; Drouffe, Jean-Michel, Statistical field theory. Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1989, ISBN 978-0-521-34058-8, MR 1175176
- Knauf, Andreas, Number theory, dynamical systems and statistical mechanics, Reviews in Mathematical Physics, 1999, 11 (8): 1027–1060, Bibcode:1999RvMaP..11.1027K, CiteSeerX 10.1.1.184.8685
, ISSN 0129-055X, MR 1714352, doi:10.1142/S0129055X99000325
- Lee, T. D.; Yang, C. N., Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model, Physical Review, 1952, 87 (3): 410–419, ISSN 0031-9007, doi:10.1103/PhysRev.87.410
- Lieb, Elliott H.; Sokal, Alan D., A general Lee-Yang theorem for one-component and multicomponent ferromagnets, Communications in Mathematical Physics, 1981, 80 (2): 153–179 [2020-03-07], ISSN 0010-3616, MR 0623156, doi:10.1007/BF01213009, (原始內容存檔於2020-07-17)
- Newman, Charles M., Zeros of the partition function for generalized Ising systems, Communications on Pure and Applied Mathematics, 1974, 27 (2): 143–159, ISSN 0010-3640, MR 0484184, doi:10.1002/cpa.3160270203
- Simon, Barry; Griffiths, Robert B., The (φ4)2 field theory as a classical Ising model, Communications in Mathematical Physics, 1973, 33 (2): 145–164, Bibcode:1973CMaPh..33..145S, CiteSeerX 10.1.1.210.9639
, ISSN 0010-3616, MR 0428998, S2CID 123201243, doi:10.1007/BF01645626
- Yang, C. N.; Lee, T. D., Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation, Physical Review, 1952, 87 (3): 404–409, ISSN 0031-9007, doi:10.1103/PhysRev.87.404