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Prog. Theor. Phys. Supplement No.157 (2005) pp. 73-76
Griffiths Inequalities in the Nishimori Line
Satoshi Morita,1
Hidetoshi Nishimori1 and
Pierluigi Contucci2
1Department of Physics, Tokyo Institute of Technology,
Tokyo 152-8551, Japan
2Dipartimento di Matematica, Università di Bologna,
40127 Bologna, Italy
Abstract:
The Griffiths inequalities for Ising spin-glass models with Gaussian
randomness of non-vanishing mean are proved using the properties of the
Gaussian distribution and the gauge symmetry of the system. These
inequalities imply that the correlation functions are non-negative and
monotonic along the Nishimori line in the phase diagram. From this
result, the existence of the thermodynamic limit for the correlation
functions and the free energy is proved under free and fixed boundary
conditions. Relations between the location of multicritical points are
also derived for different lattices.
URL :
http://ptp.ipap.jp/link?PTPS/157/73/
DOI : 10.1143/PTPS.157.73
References:
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