Pairing in quantum-critical systems: $T_c$, $Delta$, and their ratio
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abstract
We compute the ratio of the pairing gap $Delta$ at $T=0$ and $T_c$ for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility $chi (Omega) propto 1/|Omega|^gamma$ (the $gamma$ model). The limit $gamma = 0+$ ($chi (Omega) =log {|Omega|}$) describes color superconductivity, and models with $gamma >0$ describe superconductivity in a metal at the onset of charge or spin order. The ratio $2Delta/T_c$ has been recently computed numerically for $0