Abstract
Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3/2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.