Main Question or Discussion Point
More specifically, consider a Hamiltonian with a changeable parameter a. When changing a, the ground state of the system will change. In some cases, one phase crossovers to another, like in other cases, there's a phase transition. What factor determines the difference? Actually I am now working on a specific model, the Dicke model. And I want to consider the above question in this and related model. So before that, I want some general guidances about the question to get to the point quicker. Thx.