https://doi.org/10.1140/epjb/e2003-00157-8
On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory
1
Dipartimento di Fisica, Università di Roma
“La Sapienza”, Istituto Nazionale Fisica della
Materia Unità di Roma I and SMC,
P.le Aldo Moro 2, 00185 Roma, Italy
2
SMC-INFM, Dipartimento di Fisica, Università di Roma
“La Sapienza”,
P.le Aldo Moro 2, 00185 Roma, Italy
3
HAS Research Group for Theoretical Physics,
Eötvös University, Pázmány Péter sétány 1/A,
1117 Budapest, Hungary
Corresponding authors: a andrea.crisanti@phys.uniroma1.it - b tommaso.rizzo@phys.uniroma1.it - c temtam@helios.elte.hu
Received:
3
March
2003
Published online:
4
June
2003
We consider the spin-glass phase of the Sherrington-Kirkpatrick
model in the presence of a magnetic field. The series expansion of the
Parisi function q(x) is computed at high orders in powers of
and H. We find that none of the Parisi-Toulouse
scaling hypotheses on the q(x) behavior strictly holds, although
some of them are violated only at high orders. The series is
resummed yielding results in the whole spin-glass phase which are
compared with those from a numerical evaluation of the q(x). At
the high order considered, the transition turns out to be third
order on the Almeida-Thouless line, a result which is confirmed
rigorously computing the expansion of the solution near the line
at finite τ. The transition becomes smoother for
infinitesimally small field while it is third order at strictly
zero field.
PACS: 75.10.Nr – Spin-glass and other random models / 02.30.Mv – Approximations and expansions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003