ABSTRACT
This chapter explains the static scaling hypothesis, and shows how it leads to scaling laws. It discusses the topic of dynamical scaling, in which time-dependent correlations in equilibrium near the critical point exhibit scaling. The chapter introduces the topic of scaling in non-equilibrium systems. Scaling and scaling laws near the critical point of equilibrium systems follow from the renormalisation group theory, which is capable of calculating the values of the critical exponents and the form of scaling functions when used in combination with approximate methods such as perturbation theory. The static scaling hypothesis, written in the form appropriate for a magnetic system, is an attempt to encode two experimental results in one equation. Equilibrium statistical mechanics is primarily concerned with static quantities. Nevertheless, time-dependent fluctuations of a system in equilibrium fall within the scope of equilibrium statistical mechanics, through the use of the fluctuation dissipation theorem.
