Fully frustrated fractal.

Abstract

An exact technique is developed for the thermodynamic functions of an Ising system on a Sierpinsky gasket fractal, which in the antiferromagnetic case is fully frustrated. An analytic expression is obtained for the zero-temperature entropy per spin S(0) in the fully frustrated fractal, resulting in S(0)=0.493006. . . (about 50% larger than the corresponding result for the frustrated triangular lattice). Spin-spin correlations are also provided by the method and in the frustrated fractal always exhibit extremely rapid exponential decay.