Correlations and critical behavior of the q-model

Alexander V. St. John, Harsh Mathur

Published 2011-08-15, updated 2011-10-16Version 2

The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a critical point identified in earlier work these correlation functions have a universal scaling form reminiscent of thermodynamic critical phenomena. We determine the form of the universal scaling function and the associated critical exponents $\nu$ and $z$.