PHASE TRANSITIONS IN FERMI SYSTEMS

Pawel Jakubczyk (Personal webpage)

I will begin with a review of the standard theory of phase transitions in Fermi systems, starting from theworks of Hertz (1976) and Millis (1993). In this approach, the original (fermionic) degrees of freedom areintegrated our, leading to an effective bosonic order-parameter action. I will proceed to discuss some recently recognized cases (such as the electronic nematics or antiferromagnets in d=2), where this procedure fails. This may be traced back to the gapless nature of the Fermi excitations. The correct effective theory is then less conventional and requires retaining both the Fermi and order-parameter degrees of freedom.

In the last part of the lecture I will discuss the theory of neutral fermionic superfluids in d=2 formulated as a coupled Fermi-Bose renormalization-group flow. In particular, I plan to focus on the effects of the gapless order-parameter fluctuations on the Fermi self-energy across the Kosterlitz-Thouless phase transition between the superfluid and the normal phases.