This paper presents a lattice model for phases and transitions with non-invertible symmetries, using anyon chain models derived from Symmetry Topological Field Theory (SymTFT). The model is constructed from a fusion category symmetry S, with a symmetry boundary $ B_{S}^{sym} $ and an input boundary $ B_{C}^{inp} $, separated by an interface described by a C-module category M. The model is defined on a circle with periodic boundary conditions and includes a tensor product Hilbert space that can be translated into a quantum spin model. The model incorporates symmetry twisted sectors, where symmetry lines end on the interface, and describes the action of non-invertible symmetries on these sectors. The paper also discusses generalized charges for S, which are labeled by topological defects in the SymTFT. The model is applied to various symmetry categories, including Abelian group-like symmetries and $ \mathsf{Rep}(S_{3}) $, to study gapped and gapless phases and phase transitions. The lattice model is shown to capture the infrared structure of these phases and transitions, with the SymTFT providing a framework for understanding their properties. The paper also discusses the gauging of symmetries and the construction of Hamiltonians for gapped and gapless phases, using the SymTFT to derive the corresponding phases and transitions. The model is illustrated with examples, including Abelian and non-Abelian symmetries, and provides a systematic way to analyze phases and transitions in lattice models with non-invertible symmetries.This paper presents a lattice model for phases and transitions with non-invertible symmetries, using anyon chain models derived from Symmetry Topological Field Theory (SymTFT). The model is constructed from a fusion category symmetry S, with a symmetry boundary $ B_{S}^{sym} $ and an input boundary $ B_{C}^{inp} $, separated by an interface described by a C-module category M. The model is defined on a circle with periodic boundary conditions and includes a tensor product Hilbert space that can be translated into a quantum spin model. The model incorporates symmetry twisted sectors, where symmetry lines end on the interface, and describes the action of non-invertible symmetries on these sectors. The paper also discusses generalized charges for S, which are labeled by topological defects in the SymTFT. The model is applied to various symmetry categories, including Abelian group-like symmetries and $ \mathsf{Rep}(S_{3}) $, to study gapped and gapless phases and phase transitions. The lattice model is shown to capture the infrared structure of these phases and transitions, with the SymTFT providing a framework for understanding their properties. The paper also discusses the gauging of symmetries and the construction of Hamiltonians for gapped and gapless phases, using the SymTFT to derive the corresponding phases and transitions. The model is illustrated with examples, including Abelian and non-Abelian symmetries, and provides a systematic way to analyze phases and transitions in lattice models with non-invertible symmetries.