Abstract A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The
non-relativistic and ultra-relativistic d=1, 2,3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.
Fund:Project supported by the Scientific
Starting Research Fund of Central China Normal University of China,
the National Natural Science Foundation of China (Grant Nos 10675052
and 10875050) and Ministry of Education of China (Grant No