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In the present paper we extend the method to detect Pomeranchuk instabilitiesin lattice systems developed in previous works to study more generalsituations. The main result presented here is the extension of the method toinclude finite temperature effects, which allows to compute criticaltemperatures as a function of interaction strengths and density of carriers.Furthermore, it can be applied to multiband problems which would be relevant tostudy systems with spin/color degrees of freedom. Altogether, the presentextended version provides a potentially powerful technique to investigatemicroscopic realistic models relevant to e.g. the Fermi liquid to nematictransition extensively studied in connection with different materials such ascuprates, ruthenates, etc.

Pomeranchuk instabilities in multicomponent lattice systems at finite Temperature