The denominator in this expression is called the partition function : Z = ∫ ∫ D H e − − ∫ ∫ d d x [ A H 2 + Z | ∇ ∇ H | 2 + λ λ H 4 ] and the integral over all possible values of H is a statistical path integral. It integrates exp(β F) over all values of H, over all the long wavelength fourier components of the spins. F is a "Euclidean" Lagrangian for the field H. It is similar to the Lagrangian in of a scalar field in quantum field theory, the difference being that all the derivative terms enter with a positive sign, and there is no overall factor of i (thus "Euclidean").