论文信息 - Close-packed dimers on nonorientable surfaces

Close-packed dimers on nonorientable surfaces

Abstract The problem of enumerating dimers on an M × N net embedded on nonorientable surfaces is considered. We solve both the Mobius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem.

Wentao T. Lu | F. Y. Wu | Wentao Lu

[1] F. Y. Wu,et al. Dimer statistics on the Möbius strip and the Klein bottle , 1999, cond-mat/9906154.

[2] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[3] P. W. Kasteleyn. The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice , 1961 .

[4] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[5] Richard P. Stanley,et al. On dimer coverings of rectangles of fixed width , 1985, Discret. Appl. Math..

[6] T. Wu. Dimers on Rectangular Lattices , 1962 .

[7] F. Y. Wu,et al. Spanning trees on hypercubic lattices and nonorientable surfaces , 2000, Appl. Math. Lett..

[8] Y. Okabe,et al. Finite-size scaling for the ising model on the Möbius strip and the klein bottle. , 2001, Physical Review Letters.

[9] M. Fisher,et al. Dimer problem in statistical mechanics-an exact result , 1961 .

[10] J. Cardy,et al. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. , 1986, Physical review letters.

[11] Andrew G. Glen,et al. APPL , 2001 .

[12] Robert Shrock. T=0 partition functions for Potts antiferromagnets on Möbius strips and effects of graph topology , 1999 .

[13] F Y Wu,et al. Ising model on nonorientable surfaces: exact solution for the Möbius strip and the Klein bottle. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.