The communities of practice (COP) framework is useful in understanding the effort to expand physics education into professional preparation. This framework prompts physics educators and physics education researchers to consider "what counts as doing physics" that we want to prepare students for and how we can model professional physics practice in our classrooms. We argue that this focus on community omits an important consideration of the student's perceptions of the physics community, which informs how they navigate the community. We introduce the idea of a COP model to describe a student's internal representation of the community's goals and practices and their sense of membership within the community. The student develops their COP model in response to legitimate peripheral participation within the community and uses this model to extrapolate their experience of the local community to the global community. We describe how this construct shares similarities with other frameworks but retains distinct features that make it a helpful tool for analysis. We demonstrate the use of the COP model in the review of student interviews about the use of computational practices in the physics community. The COP model helps us interpret student responses in terms of their COP models' alignment and misalignment with the physics community. We discuss implications for instruction and reflect on the utility of the COP-model construct.