Thermal stability conditions of a weakly interacting Fermi gas in a weak magnetic field

On the basis of the results derived from pseudopotential method and ensemble theory, thermal stability of a weakly interacting Fermi gas in a weak magnetic field is studied by using analytical method of thermodynamics. The exact analytical expressions of stability conditions at different temperatures are given, and the effects of interactions as well as magnetic field on the stability of the system are discussed. It is shown that there is an upper-limit magnetic field for the stability of the system at low temperatures, and there is an attractive dividing value at high temperatures. If attractive interaction is lower than the critical value, the stability of the system has no request for magnetic field, but if attractive interaction is higher than the dividing value, a lower-limit magnetic field exists for the stability of the system.