In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature
effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to e.g. the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus providing a powerful tool for the search of exo
tic phases. We test it by applying it to a lattice electron model with interactions leading to $s$ and d-wave instabilities.
