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Test of Many-Body Scattering Formalisms by Application to AN Exactly Soluble Model.

A. J. Lewanski

Published Jan 1, 1978• 0 citations
OpenAlex

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The exactly soluble R(8) model of Krumlinde and Szyma\ifmmode \acute{n}\else \'{n}\fi{}ski is used as a testing ground for three many-body methods applied to the yrast band: (i) the self-consistent cranking model, (ii) self-consistent cranking plus random-phase approximation, and (iii) variation after projection of particle number. All three methods agree very well with exact results outside of the critical region. The behavior in the critical region is examined in detail.NUCLEAR STRUCTURE Many-body methods, solvable model, high-spin states.

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Two-Dimensional Ising Model as a Soluble Problem of Many Fermions

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The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble and shows a phase transition. Although the exact solution in the absence of an external magnetic field was first given almost twenty years ago in a famous paper by Onsager1 using the theory of Lie algebras, the flow of papers on both approximate and exact methods has remained strong to this day.2 One reason for this has been the interest in testing approximate methods on an exactly soluble problem. A second reason, no doubt, has been the considerable formidability of the Onsager method. The simplification achieved by Bruria Kaufman3 using the theory of spinor representations has diminished, but not removed, the reputation of the Onsager approach for incomprehensibility, while the subsequent application of this method by Yang4 to the calculation of the spontaneous magnetization has, if anything, helped to restore this reputation.

Reviews of Modern Physics•Jul 1, 1964•935 citations

Many-body scattering problem

Israel Michael Sigal

Springer eBooks•Apr 6, 2008•0 citations
The exactly soluble R(8) model of Krumlinde and Szyma\ifmmode \acute{n}\else \'{n}\fi{}ski is used as a testing ground for three many-body methods applied to the yrast band: (i) the self-consistent cranking model, (ii) self-consistent cranking plus random-phase approximation, and (iii) variation after projection of particle number. All three methods agree very well with exact results outside of the critical region. The behavior in the critical region is examined in detail.NUCLEAR STRUCTURE Many-body methods, solvable model, high-spin states.
The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble and shows a phase transition. Although the exact solution in the absence of an external magnetic field was first given almost twenty years ago in a famous paper by Onsager1 using the theory of Lie algebras, the flow of papers on both approximate and exact methods has remained strong to this day.2 One reason for this has been the interest in testing approximate methods on an exactly soluble problem. A second reason, no doubt, has been the considerable formidability of the Onsager method. The simplification achieved by Bruria Kaufman3 using the theory of spinor representations has diminished, but not removed, the reputation of the Onsager approach for incomprehensibility, while the subsequent application of this method by Yang4 to the calculation of the spontaneous magnetization has, if anything, helped to restore this reputation.