Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices

•Mixed spin-(1/2, 1) Ising model on two fully frustrated lattices is exactly solved.•Order-from-disorder effect is convincingly evidenced by a rigorous calculation.•Reentrant phase transitions with 2 or 3 successive critical points are found.•Spontaneous order may coexist with a disorder within the ground state.

The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin- 1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered–disordered ground state, which manifests itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behavior including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.