Fermionic Ising glasses with BCS pairing interaction in the presence of a transverse field

Abstract

In the present work we have analyzed a fermionic infinite-ranged Ising spin glass with a local BCS coupling in the presence of transverse field. This model has been obtained by tracing out the conduction electrons degrees of freedom in a superconducting alloy. The transverse field is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spins operators are represented by bilinear combination of Grassmann fields. The problem can be solved by combining previous approaches used to study a fermionic Heisenberg spin glass and a Ising spin glass in a transverse field. The results are shown in a phase diagram T/ J versus Γ/ J ( J is the standard deviation of the random coupling J ij ) for several values of g (the strength of the pairing interaction). For small g, the line transition T c( Γ) between the normal-paramagnetic phase and the spin glass phase decreases when Γ increases, until it reaches a quantum critical point. For increasing g, a PAIR phase (where there is formation of local pairs) has been found which disappears when it is close to Γ c showing that the transverse field tends to inhibit the PAIR phase.