Eur. Phys. J. B 9, 5-13 (1999)
https://doi.org/10.1007/s100510050736

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

¹ Departamento de Matematica, Universidade Federal de Santa Maria, 97119-900 Santa Maria, RS, Brazil
² Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, C.P. 15051 91501-970 Porto Alegre, RS, Brazil

Received: 14 May 1998
Published online: 15 May 1999

Abstract

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line that ends at a tricritical point , , from where it becomes a first order transition line that meets the line of second order transitions at that separates the NP and the SG phases. For the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in .