2000/07/20 by Wentao Lu, Wentao T. Lu, F. Y. Wu · 5 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Combinatorics #Condensed matter physics #Conformal map #Geometry #Ising model #Klein bottle #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Minimal models #Partition function (quantum field theory) #Periodic boundary conditions #Physics #Pure mathematics #Quantum many-body systems #Quantum mechanics #Quartic function #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Toroid #Torus #cond-mat.stat-mech #hep-th #math-ph #math.CO #math.MP
paper · pdf · doi:10.1103/physreve.63.026107
published as Phys.Rev. E63 (2001) 026107 · 8 pages, 3 eps figures
arxiv created 2000/07/20 · openalex publication_date 2001/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.