  In this work, based on some mathematical results obtained by Yamabe, Osgood,
Phillips and Sarnak, we demonstrate that in dimensions three and higher the
famous Ginzburg-Landau equations used in theory of phase transitions can be
obtained (without any approximations) by minimization of the Riemannian-type
Hilbert-Einstein action functional for pure gravity in the presence of
cosmological term. We use this observation in order to bring to completion the
work by Lifshitz (done in 1941) on group-theoretical refinements of the Landau
theory of phase transitions. In addition, this observation allows us to develop
a systematic extension to higher dimensions of known string-theoretic path
integral methods developed for calculation of observables in two dimensional
conformal field theories.

General Relativity and Quantum Cosmology