Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interplay between superconductivity and non-Fermi liquid at a
  quantum-critical point in a metal: V. The $\gamma$ model and its phase
  diagram. The case $\gamma =2$   This paper is a continuation and a partial summary of our analysis of the
pairing at a quantum-critical point (QCP) in a metal for a set of
quantum-critical systems, whose low-energy physics is described by an effective
model with dynamical electron-electron interaction $V(\Omega_m) = ({\bar
g}/|\Omega_m|)^\gamma$ (the $\gamma$-model). Examples include pairing at the
onset of various spin and charge density-wave and nematic orders and pairing in
SYK-type models. In previous papers, we analyzed the physics for $\gamma <2$.
We have shown that the onset temperature for the pairing $T_p$ is finite, of
order ${\bar g}$, yet the gap equation at $T=0$ has an infinite set of
solutions within the same spatial symmetry. As the consequence, the
condensation energy $E_c$ has an infinite number of minima. The spectrum of
$E_c$ is discrete, but becomes more dense as $\gamma$ increases. Here we
consider the case $\gamma =2$. The $\gamma=2$ model attracted special interest
in the past as it describes the pairing by an Einstein phonon in the limit when
the dressed phonon mass $\omega_D$ vanishes. We show that for $\gamma =2$, the
spectrum of $E_c$ becomes continuous. We argue that the associated gapless
"longitudinal" fluctuations destroy superconducting phase coherence at a finite
$T$, such that at $0<T< T_p$ the system displays pseudogap behavior. We show
that for each gap function from the continuum spectrum, there is an infinite
array of dynamical vortices in the upper half-plane of frequency. For the
electron-phonon case, our results show that $T_p =0.1827 {\bar g}$, obtained in
earlier studies, marks the onset of the pseudogap behavior of preformed pairs,
while the actual superconducting $T_c$vanishes at $\omega_D \to 0$.

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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph