Self-similarity in the classification of finite-size scaling functions for toroidal boundary conditions

Virginia TechLiaw, T. M.Huang, M. C.Luo, Y. P.Lin, S. C.Chou, Y. L.Deng, Y.2014-01-172014-01-172008-01Liaw, Tsong-Ming ; Huang, Ming-Chang ; Luo, Yu-Pin ; et al., Jan 2008. "Self-similarity in the classification of finite-size scaling functions for toroidal boundary conditions," PHYSICAL REVIEW E 77(1) Part 1: 010101. DOI: 10.1103/PhysRevE.77.0101011539-3755http://hdl.handle.net/10919/24886The conventional periodic boundary conditions in two dimensions are extended to general boundary conditions, prescribed by primitive vector pairs that may not coincide with the coordinate axes. This extension is shown to be unambiguously specified by the twisting scheme. Equivalent relations between different twist settings are constructed explicitly. The classification of finite-size scaling functions is discussed based on the equivalent relations. A self-similar pattern for distinct classes of finite-size scaling functions is shown to appear on the plane that parametrizes the toroidal geometry.en-USIn Copyrightising-modelklein bottlemobius strippercolationsystemsuniversalitylatticeszerosPhysicsSelf-similarity in the classification of finite-size scaling functions for toroidal boundary conditionsArticle - Refereedhttp://link.aps.org/doi/10.1103/PhysRevE.77.010101Physical Review Ehttps://doi.org/10.1103/PhysRevE.77.010101