Lack of monotonicity in spin glass correlation functions
  We study the response of a spin glass system with respect to the rescaling of its interaction random variables and investigate numerically the behaviour of the correlation functions with respect to the volume. While for a ferromagnet the local energy correlation functions increase monotonically with the scale and, by consequence, with respect to the volume of the system we find that in a general spin glass model those monotonicities are violated. 
Pierluigi Contucci, Francesco Unguendoli, Cecilia Vernia