Effect of thermal ground state correlations on the statistical properties of the Lipkin model
A.I. Vdovin - A.N. Storozhenko
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Received: 4 January 1999 / Revised version: 10 March 1999 Communicated by P. Schuck
Abstract
The renormalized random phase approximation for hot finite Fermi systems
is evaluated with the use of the thermo field dynamics formalism. This approximation
treats vibrations of a hot finite Fermi system as harmonic ones but
takes into account the Pauli principle in a more proper way than the
usual thermal RPA, thus incorporating a new type of correlations in a
thermal ground state. To demonstrate advantages of the
approximation and to analyze a range of its validity, it is applied to
the exactly solvable Lipkin model. A comparison is made with the exact grand
canonical ensemble calculations, results of the thermal Hartree - Fock
approximation and the thermal random phase approximation.
The intrinsic energy of the system,
the heat capacity, the average value of the quasispin operator z-projection
and the particle number variance are calculated as functions of temperature.
On the whole, the thermal renormalized RPA appears to be a better approximation
than the other two. Its advantage is especially evident in the vicinity of
the phase transition point. It is found that within TRRPA the phase
transition occurs at lower temperature than in THFA and TRPA.
PACS
21.60.Jz Hartree-Fock and random-phase approximations -
11.10.Wx Finite-temperature field theory
Copyright Springer-Verlag
