Topological variants of lattice field models

The conventional Ising model is generalised so as to introduce a topological frustration for both ferromagnetic and antiferromagnetic cases. This generalisation is extended to a broad class of lattice field models, including the conventional XY model and classical Heisenberg model as special cases. Twisted external fields are also introduced in a manner symmetrical with respect to the intrinsic fields. The partition function and the two-point correlation function are explicitly determined for several varieties of twisted 1-dimensional chains with zero external field. Cohomological and fibre bundle interpretations are discussed.