Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

摘要

The competition among spin glass (SG), antiferromagnetism (AF) and localpairing superconductivity (PAIR) is studied in a two-sublattice fermionic Isingspin glass model with a local BCS pairing interaction in the presence of anapplied magnetic transverse field $\Gamma$. In the present approach, spins indifferent sublattices interact with a Gaussian random coupling with anantiferromagnetic mean $J_0$ and standard deviation $J$. The problem isformulated in the path integral formalism in which spin operators arerepresented by bilinear combinations of Grassmann variables. The saddle-pointGrand Canonical potential is obtained within the static approximation and thereplica symmetric ansatz. The results are analysed in phase diagrams in whichthe AF and the SG phases can occur for small $g$ ($g$ is the strength of thelocal superconductor coupling written in units of $J$), while the PAIR phaseappears as unique solution for large $g$. However, there is a complex linetransition separating the PAIR phase from the others. It is second order athigh temperature that ends in a tricritical point. The quantum fluctuationsaffect deeply the transition lines and the tricritical point due to thepresence of $\Gamma$.