Gaussian field theory
= Gaussian field theory
A Gaussian field theory has a free energy quadratic in its field modes. If $H_0=\sum_{\mathbf q}^{+}J(q)|\phi_{\mathbf q}|^2$ for a real field, then $\langle|\phi_{\mathbf q}|^2\rangle=J(q)^{-1}$ and its partition function is a product of elementary Gaussian integrals.