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.
REFERENCES
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.
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