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We study the competition between the nematic and the hexatic phases of atwo-dimensional spinless Fermi fluid near Pomeranchuk instabilities. We showthat the general phase diagram of this theory contains a bicritical point wheretwo second order lines and a first order nematic/hexatic phase transition meettogether. We found that at criticality, and deep inside the associated symmetrybroken phases, the low energy theory is governed by a dissipative cubic mode,even near the bicritical point where nematic and hexatic fluctuations cannot bedistinguished due to very strong dynamical couplings.

Competition between Pomeranchuk instabilities in the nematic and hexatic channels in a two-dimensional spinless Fermi fluid