Scaling laws at the critical point

S. Davatolhagh

Published 2005-07-27, updated 2006-06-19Version 2

There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\eta'$.