Discussion Overview
The discussion revolves around the factors that determine whether a system experiences a crossover or a phase transition when a parameter in the Hamiltonian is varied. Participants explore this question in the context of theoretical models, particularly the Dicke model, and consider implications for thermodynamic limits.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant notes that changing a parameter in the Hamiltonian can lead to different behaviors, specifically crossovers or phase transitions, and seeks general guidance on this distinction.
- Another participant suggests that the rate of change of the parameter (da/dt) influences whether a crossover or phase transition occurs, with fast changes leading to crossovers and slow changes potentially resulting in phase transitions.
- A participant defines phase transitions as characterized by non-analytic changes, contrasting them with crossovers, which do not exhibit such behavior. They highlight complications such as finite size effects and the difficulty of tuning systems precisely to phase transitions.
- One participant agrees with the idea that energy level crossing corresponds to phase transitions, while avoided crossings correspond to crossovers. They mention that mixing of states can lead to gaps and discuss factors that can forbid this mixing, such as symmetry differences and topological indices.
- Another participant affirms that level crossings are associated with phase transitions and references a formalism involving quantum fidelity to support this perspective.
Areas of Agreement / Disagreement
Participants express differing views on the definitions and implications of crossovers versus phase transitions. While some agree on the relationship between energy level crossings and phase transitions, there is no consensus on the broader implications or specific conditions that govern these phenomena.
Contextual Notes
Participants acknowledge limitations related to finite size effects and the challenges of observing singular behaviors in real systems, although some focus on theoretical frameworks under the thermodynamic limit.
Who May Find This Useful
This discussion may be of interest to researchers and students in theoretical physics, particularly those studying phase transitions, quantum mechanics, and related models in condensed matter physics.