To the Topology of KramersWannier Duality
Abstract
We show that for an evendimensional hypercubic lattice one can modify the construction of a dual lattice to have the correspondence edgeedge instead of the conventional correspondence edge(d1)dimensional face. This gives a straightforward generalization of KramersWannier duality for an evendimensional Ising model. In the same way as the partition function for the 2D Ising model is related to a sum over paths on a torus, higherdimensional models involve sums over paths on Riemannian surfaces of higher genus. The critical temperature can be located only in the d=2 case in which all topological effects disappear from the thermodynamic limit. The duality in higher dimensions, however, being weak, leads nevertheless to some interesting relations for sums over paths on Riemannian surfaces, which can be considered as a topological characteristic of a critical point.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 1994
 DOI:
 10.1142/S0217751X94001126
 Bibcode:
 1994IJMPA...9.2755M