Correlation Inequalities for Spin Glasses
Disordered Systems and Neural Networks
2009-11-11 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences include existence of the thermodynamic limit for the pressure and bounds on the surface pressure. We also describe other conjectured inequalities for such systems.
Keywords
Cite
@article{arxiv.cond-mat/0612371,
title = {Correlation Inequalities for Spin Glasses},
author = {Pierluigi Contucci and Joel Lebowitz},
journal= {arXiv preprint arXiv:cond-mat/0612371},
year = {2009}
}