CRITICAL FREE-ENERGY OF A MOBIUS STRIP

Explicit expressions for the free energy of the dimer model on finite quadratic and honeycomb lattices embedded in a Mobius strip are obtained. They allow us to establish the existence of a simple relationship between the partition functions on a Mobius strip and on a cylinder. The properties of the finite size correction term D at critically, whose universality is predicted by conformal theories, are studied in the limit of an infinitely large system with a fixed width-to-length ratio lambda. As expected, in the limit of an infinitely narrow Mobius strip (lambda --> infinity) the D-term tends to the value for a strip with free edges. In the opposite limit of an infinitely wide Mobius strip the term D is found again to tend to the value for a strip with free edges. The free energy of twisting G is defined as the difference between the free energies for a cylinder and for the corresponding Mobius strip. The behavior of G as a function of lambda is studied too.