Phase bifurcations of electron gas at the conditions of diamagnetic instability

In a framework of catastrophe theory we investigate the equilibrium set for an electron gas at the conditions of strong dHvA effect and show that discontinuities accompanied the diamagnetic phase transition (DPT) is handled by Riemann-Hugoniot catastrophe. We show that the applicability of the standard condition for observation of DPT a≥1 where a is the differential magnetic susceptibility is valid only in the nearest vicinity of the centre of dHvA period corresponding to triple degenerate point, but for arbitrary value of magnetic field in every period of dHvA oscillations this condition is modified in accordance with the bifurcation set of cusp catastrophe. While at the center of dHvA period the symmetrical supercritical pitchfork bifurcation gives rise to the second-order phase transition on temperature, the deviation of magnetic field from the value corresponding to the centre of dHvA period results in the change of the phase transition order from the second to the first one both on temperature and magnetic field. In the framework of developed theory we obtain good agreement with available experimental data.