The denominator in this expression is called the "partition function", 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", the only difference between this and the quantum field theory of a scalar field being that all the derivative terms enter with a positive sign, and there is no overall factor of "i".