I have a couple of questions on the relation of RG and phase transitions. I've heard in many sources that the theory of most transitions (excluding novel phase transitions like Quantum Critical transitions) is essentially captured by RG, but this insight is not clear to me. I have studied RG in the context of QFT and have an okay understanding of phase transitions.
My current understanding is that RG tells us that we can change the scale of the system to modify the parameters in the Hamiltonian, and the fixed points of this transformation are the locations of phase transitions. A couple of questions:
- In normal phase transitions, the parameter that takes us to a transition in the temperature. So is the temperature related to the scaling parameter in the RG analysis? Is it the temperature that moves us on plot of our coupling constants?
- Do all fixed points of the RG transformation correspond to phase transitions?
