C^*-basic construction on field algebras of G-spin models

Let G be a finite group. Starting from the field algebra F of G-spin models, we show that the C^*-basic construction for the field algebra F and the D(G)-invariant subalgebra of F can be represented as the crossed product C^*-algebra F ⋊ D(G). Moreover, under the naturalD(G)-module action on F ⋊ D(G), the iterated crossed product C^*-algebra can be obtained, which is C^*-isomorphic to the C^*-basic construction for F ⋊ D(G) and the field algebra F. In addition, it is proved that the iterated crossed product C^*-algebra is a new field algebra, and the concrete structures with the order and disorder operators are given.