Fermi Liquid Singularities and Quantum Criticality
or Influence of Generic Soft Modes on Quantum Critical Behavior 
University of Oregon 
Leading scaling behavior usual FL properties
Disordered systems: ph excitations diffusive (scale dimension d2)
Weaklocalization type nonanalytic corrections

Derived in perturbation theory long before RG
treatment
( Altshuler & Aronov )
Weaklocalization effects not usually thought of as corrections to scaling, but they emerge from standard scaling arguments in the vicinity of a (disordered) FL fixed point ( TRK & DB )
Analogous singularities in other observables, and in Tdependences
Appears via integral over diffusive modes:
Clean analogies to weaklocalization corrections

Early attempts (Landau theory, perturbation theory) led to confusion
Lately firmly established by perturbation theory
( DB, TRK & TV; Chitov & Millis; Chubukov & Maslov )
Soft modes, resulting nonanalyticities occur in an entire phase
These are generic soft modes
How big a deal? (After all, these are just standard corrections to scaling!)
Coupling between generic soft modes and OP fluctuations
Simple LGW theory inadequate, coupled field theory is needed
Breakdown of Hertz's LGW program
This can happen at classical transitions, too (e.g., compressible magnets), but
Examples: Various magnetic QPTs in metals
AFM QPT ( Abanov & Chubukov ; Pepin et al )
2nd order in other materials (e.g., ZrZn_{2}) with meanfield exponents
T^{3/2} dependence of the resisitivity in a whole region in the PM phase
Also shows resistivity T^{n} with n ~ 1.5 in the PM phase ( Bauer et al )
Theory (the theory meister just can't resist):
Clean case:
2nd order transition: Feedback effects suppress fluctuations that lead to 1st order transition Nonmean field 2nd order transition
Upper critical dimension d_{c}^{+} = 3 ( not 1 as in Hertz theory). This explains observation of meanfield exponents even though Hertz theory breaks down.
Disordered case:
Strongly nonmean field, in agreement with experiment
Critical behavior in d=3 known exactly: Longranged
fluctuations
Gaussian critical fixed point (almost, various DIVs)
T^{3/2} behavior of resistivity: Open question
Breakdown of FL, or corrections to scaling?