Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions in the pseudogap Anderson and Kondo models: Critical
  dimensions, renormalization group, and local-moment criticality   The pseudogap Kondo problem, describing quantum impurities coupled to
fermionic quasiparticles with a pseudogap density of states, rho(omega) ~
|omega|^r, shows a rich zero-temperature phase diagram, with different screened
and free moment phases and associated transitions. We analyze both the
particle-hole symmetric and asymmetric cases using renormalization group
techniques. In the vicinity of r=0, which plays the role of a lower-critical
dimension, an expansion in the Kondo coupling is appropriate. In contrast, r=1
is the upper-critical dimension in the absence of particle-hole symmetry, and
here insight can be gained using an expansion in the hybridization strength of
the Anderson model. As a by-product, we show that the particle-hole symmetric
strong-coupling fixed point for r<1 is described by a resonant level model, and
corresponds to an intermediate-coupling fixed point in the renormalization
group language. Interestingly, the value r=1/2 plays the role of a second
lower-critical dimension in the particle-hole symmetric case, and there we can
make progress by a novel expansion performed around a resonant level model. The
different expansions allow a complete description of all critical fixed points
of the models and can be used to compute a variety of properties near
criticality, describing universal local-moment fluctuations at these impurity
quantum phase transitions.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
2
The categories of this paper are: math
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom