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Physical Review C

Phase transitions in exactly soluble models

Guillermo H. Bozzolo, J. Núñez, Angelo Plastino

Published Dec 1, 1982• 4 citations
Publisher

Abstract

A linearized version of the Hartree-Fock method is reinvestigated in order to develop a new technique for the study of phase transitions. This is studied with reference to an exactly soluble model, yielding excellent results.NUCLEAR STRUCTURE Phase transitions. Approximate many body methods applied to a soluble model.
DOI
10.1103/physrevc.26.2692

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•Jan 19, 2015•0 citations
We test the coherent correlated pair method with the soluble SU(3) Hamiltonian of Li, Klein, and Dreizler. We compare the results for the ground state energy with the exact solution and with the Hartree-Fock results as a function of coupling parameters and number of particles. For all cases the coherent correlated pair method yields the better upper bound to the ground state energy.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bounds to ground state energies; applications to exactly soluble SU(3) NNN-fermion model.
We develop a method for treating the NNN-fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bound to ground state energy; applications to soluble NNN-fermion models.
The "phase transitions" predicted within finite microscopic systems by Hartree-Fock-Bogoliubov (HFB) and aspects of the use of the associated broken-syrometry bases in the random-phase approximation (RPA) are considered using soluble models-Evidence is presented in support of the conjecture that the success of these techniques lies in the fact that they mimic singularities in the dependence on interaction strengths of the exact solution.This conjecture provides a natural explanation for why such methods fail close to a point where a phase transition occurs and indicates possible directions for improvement.Phase diagrams at both zero and finite temperature are determined, and simple analytic expressions for the way in which critical scrcn;the scale with particle number are found.It is shown that the ''phase transitions" predicted at finite temperature are relevant.A connection between the singularities referred to above and real phase transitions found in the thermodynamic limit is discussed.It is found that only stable bases can be used in an RPA calculation.This is in particular true for those RPA modes which are not associated with the onset of instability of the basis; these modes do not describe any excited state when tht. basis is unstable.Outside transitional regions certain undesirable features of HFB are unearthed, notably that the HFB ground state energy is not necessarily an upper bound to the exact ground state energy.The effectiveness in this regime of the Hartree-Fock Seniority approximation as a substitute to projection methods is ■ -■■.ated.