PMID: 11308542Apr 20, 2001Paper

Ising model on nonorientable surfaces: exact solution for the Möbius strip and the Klein bottle

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
W T Lu, F Y Wu

Abstract

Closed-form expressions are obtained for the partition function of the Ising model on an MxN simple-quartic lattice embedded on a Möbius strip and a Klein bottle. The solutions all lead to the same bulk free energy, but for finite M and N the expressions are different depending on whether the strip width M is odd or even. Finite-size corrections at criticality are analyzed and compared with those under cylindrical and toroidal boundary conditions. Our results are consistent with the conformal field prediction of a central charge c=1/2, provided that the twisted Möbius boundary condition is regarded as a free or fixed boundary.

References

Feb 17, 1986·Physical Review Letters·H W BlöteM P Nightingale

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Citations

Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Y Okabe, N Kawashima
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T AntalZ Rácz
Jan 20, 2018·Physical Review. E·Armen PoghosyanRalph Kenna
Jun 29, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tsong-Ming LiawFeng-Yin Li
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tsong-Ming LiawYoujin Deng
Dec 12, 2001·Physical Review Letters·T AntalZ Rácz
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Ming-Chang Huang
Jan 13, 2018·Physical Review Letters·Hong-Hao Tu
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, R Kenna
Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ming-Chya WuN Sh Izmailian
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V EislerF van Wijland
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I Lyberg
May 23, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ming-Chya Wu

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