Finite-Size Scaling for the Ising Model on the Möbius Strip and the Klein Bottle

We study the finite-size scaling properties of the Ising model on the Möbius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function p\(m\) for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at T = T_c for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.