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
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 Jij, 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
.
PACS: 05.50.+q – Lattice theory and statistics; Ising problems / 64.60.Cn – Order disorder transformations; statistical mechanics of model systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999