三角形晶格Ising 模型的Julia 集
Julia Set of the Triangular Lattice Ising Model
DOI: 10.12677/PM.2021.1111204, PDF, HTML, 下载: 350  浏览: 2,085  国家自然科学基金支持
作者: 杨存基:大理大学数学与计算机学院,云南 大理
关键词: Ising 模型Julia 集Hausdorf维数连通性Ising Model Julia Set Hausdorff Dimension Connectivity
摘要: 本文刻画了三角形晶格上Ising 模型重整化变换函数Julia 集的连通性和Hausdorff 维数。
Abstract: In this paper, we study the connectivity and the Hausdorff dimension of Julia sets in triangular lattice Ising model.
文章引用:杨存基. 三角形晶格Ising 模型的Julia 集[J]. 理论数学, 2021, 11(11): 1810-1820. https://doi.org/10.12677/PM.2021.1111204

参考文献

[1] Yang, C.N. and Lee, T.D. (1952) Statistical Theory of Equations of State and Phase Transi- tions. I. Theory of Condensation. Physical Review, 87, 404-409.
https://doi.org/10.1103/PhysRev.87.404
[2] Yang, C.N. and Lee, T.D. (1952) Statistical Theory of Equations of State and Phase Transi- tions. II. Lattice Gas and Ising Model. Physical Review, 87, 410-419.
https://doi.org/10.1103/PhysRev.87.410
[3] McMullen, C.T. (1994) Complex Dynamics and Renormalization. Princeton University Press, Princeton, NJ.
[4] Qiao, J.Y. (2005) Julia Sets and Complex Singularities in Diamond-Like Hierarchical Potts Models. Science in China Series A: Mathematics, 48, 388-412.
[5] Qiao, J.Y. and Li, Y.H. (2001) On Connectivity of Julia Sets of Yang-Lee Zeros. Communica- tions in Mathematical Physics, 222, 319-326.
https://doi.org/10.1007/s002200100507
[6] Yang, C.J. and Wang, S.M. (2020) The Singularities in Renormalization of Triangular Net Ising Model. Journal of Dali University, 5, 1-8.
[7] Onsager, L. (1944) Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Physical Review, 65, 117-149.
https://doi.org/10.1103/PhysRev.65.117
[8] Yang, C.N. (1952) The Spontaneous Magnetization of a Two-Dimensional Ising Model. Physical Review, 85, 808-816.
https://doi.org/10.1103/PhysRev.85.808
[9] Niemeijer, Th. and van Leeuwen, J.M.J. (1973) Wilson Theory for Spin Systems on a Triangu- lar Lattice. Physical Review Letters, 31, 1411.
https://doi.org/10.1103/PhysRevLett.31.1411
[10] Beardon, A.F. (1991) Iteration of Rational Functions. Springer-Verlag, New York, Berlin.
[11] Carleson, L. and Gamelin, T.W. (1993) Complex Dynamics. Springer-Verlag, New York, Berlin.
https://doi.org/10.1007/978-1-4612-4364-9
[12] Milnor, J. (2006) Dynamics in One Complex Variable. 3rd Edition, Princeton University Press, New Jersey.
[13] Ren, F.Y. (1996) Complex Analysis Dynamics. Fudan University Press, Shanghai. (In Chinese)
[14] Zheng, J.H. (2006) Dynamics of Meromorphic Functions. Tsinghua University Press, Beijing.
[15] Stallard, G.M. (1994) The Hausdorff Dimension of Julia Sets of Meromorphic Functions. Jour- nal of the London Mathematical Society, 49, 218-295.
https://doi.org/10.1112/jlms/49.2.281
[16] Stallard, G.M. (1999) The Hausdorff Dimension of Julia Sets of Meromorphic Functions II. Journal of the London Mathematical Society, 60, 874-859.
https://doi.org/10.1112/S0024610799008029
[17] Prztycki, F., Urbanski, M. and Zdunik, A. (1990) Harmonic, Gibbs and Hausdorff Measures on Repellers for Holomorphic Maps, II. Studia Mathematica, 97, 189-225.
https://doi.org/10.4064/sm-97-3-189-225
[18] Zdunik, A. (1991) Harmonic Measure versus Hausdorff Measures on Repellers for Holomorphic Maps. Transactions of the American Mathematical Society, 326, 633-652.
https://doi.org/10.1090/S0002-9947-1991-1031980-0
[19] Bolsch, A. (1999) Periodic Fatou Components of Meromorphic Functions. Bulletin of the Lon- don Mathematical Society, 31, 543-555.
https://doi.org/10.1112/S0024609399005950
[20] Noshiro, K. (1960) Cluster Sets. Spring-Verlag, Berlin, 144.
https://doi.org/10.1007/978-3-642-85928-1
[21] Baker, I.N. (1987) Wandering Domains for Maps of the Punctured Plane. Annales Academiae Scientiarum Fennicae: Series A. I. Mathematica, 12, 191-198.
https://doi.org/10.5186/aasfm.1987.1204