Abstract
The duality transformations are carried out for both the pure Ising spin system and the Ising spin system interacting with Z 2 gauge fields. For the Ising model embedding on a surface whose genus is larger than zero, we find that there are topologic excitons which do not appear in the planar model. When gauge fields are included in the model, the topologic excitons are swept away. Instead, an external field emerges in the dual model after integrating out the gauge fields.
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