Mechanisms driving alteration of the Landau state in the vicinity of a   second-order phase transition
  The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation $\epsilon(p)=\mu$, a condition that ordinarily has the Fermi momentum $p_F$ as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition. 
M. Baldo, V. V. Borisov, J. W. Clark, V. A. Khodel, and M. V. Zverev