It is proved that the variance of a spin overlap vanishes in the infinite volume limit of the random field Ginzburg-Landau model whose truncated two point correlation functions satisfy the Fortuin-Kasteleyn-Ginibre inequality.

1.
M.
Aizenman
and
P.
Contucci
, “
On the stability of quenched state in mean-field spin glass models
,”
J. Stat. Phys.
92
,
765
783
(
1997
).
2.
S.
Chatterjee
, “
Absence of replica symmetry breaking in the random field Ising model
,”
Commun. Math. Phys.
337
,
93
102
(
2015
).
3.
S.
Chatterjee
, “
The Ghirlanda-Guerra identities without averaging
,” preprint arXiv:0911.4520 (
2009
).
4.
S.
Chatterjee
, “
Disorder chaos and multiple valleys in spin glasses
,” preprint arXiv:0907.3381 (
2009
).
5.
P.
Contucci
and
C.
Giardinà
, “
Spin-glass stochastic stability: A rigorous proof
,”
Ann. Henri Poincare
6
,
915
923
(
2005
).
6.
P.
Contucci
and
C.
Giardinà
, “
The Ghirlanda-Guerra identities
,”
J. Stat. Phys.
126
,
917
931
(
2007
).
7.
P.
Contucci
and
C.
Giardinà
,
Perspectives on Spin Glasses
(
Cambridge University Press
,
2012
).
8.
P.
Contucci
,
C.
Giardinà
, and
J.
Pulé
, “
The infinite volume limit for finite dimensional classical and quantum disordered systems
,”
Rev. Math. Phys.
16
,
629
638
(
2004
).
9.
P.
Contucci
and
J. L.
Lebowitz
, “
Correlation inequalities for quantum spin systems with quenched centered disorder
,”
J. Math. Phys.
51
,
023302-1
023302-
6
(
2010
).
10.
P.
Contucci
,
E.
Mingione
, and
S.
Starr
, “
Factorization properties in d-dimensional spin glasses. Rigorous results and some perspectives
,”
J. Stat. Phys.
151
,
809
829
(
2013
).
11.
C. M.
Fortuin
,
P. W.
Kasteleyn
, and
J.
Ginibre
, “
Correlation inequalities on some partially ordered sets
,”
Commun. Math. Phys.
22
,
89
103
(
1971
).
12.
S.
Ghirlanda
and
F.
Guerra
, “
General properties of overlap probability distributions in disordered spin systems. Towards parisi ultrametricity
,”
J. Phys. A: Math. Gen.
31
,
9149
9155
(
1998
).
13.
R. B.
Griffiths
, “
Spontaneous magnetization in idealized ferromagnets
,”
Phys. Rev.
152
,
240
246
(
1966
).
14.
C.
Itoi
, “
General properties of overlap operators in disordered quantum spin systems
,”
J. Stat. Phys.
163
,
1339
1349
(
2016
).
15.
C.
Itoi
, “
Absence of replica symmetry breaking in transverse and longitudinal random field Ising model
,”
J. Stat. Phys.
170
,
684
699
(
2018
).
16.
F.
Krzakala
,
F.
Ricci-Tersenghi
, and
L.
Zdeborova
, “
Elusive spin-glass phase in the random field Ising model
,”
Phys. Rev. Lett.
104
,
207208
(
2010
).
17.
F.
Krzakala
,
F.
Ricci-Tersenghi
,
D.
Sherrington
, and
L.
Zdeborova
, “
No spin glass phase in ferromagnetic random field and random temperature scalar Ginzburg-Landau models
,”
J. Phys. A: Math. Theor.
44
,
042003
(
2011
).
18.
G.
Parisi
, “
A sequence of approximate solutions to the S-K model for spin glasses
,”
J. Phys. A: Math. Gen.
13
,
L
115
(
1980
).
19.
S.
Sherrington
and
S.
Kirkpatrick
, “
Solvable model of spin glass
,”
Phys. Rev. Lett.
35
,
1792
1796
(
1975
).
20.
M.
Talagrand
, “
The Parisi formula
,”
Ann. Math.
163
,
221
263
(
2006
).
21.
M.
Talagrand
,
Mean Field Models for Spin Glasses
(
Springer
,
Berlin
,
2011
).
You do not currently have access to this content.