Spin-Boson Systems: One-Dimensional Equivalents and the Kondo Problem

M. Blume; V. J. Emery; A. Luther

doi:10.1103/PhysRevLett.25.450

Spin-Boson Systems: One-Dimensional Equivalents and the Kondo Problem

M. Blume, V. J. Emery, and A. Luther

Phys. Rev. Lett. 25, 450 – Published 17 August 1970

Abstract

The partition function for a spin ½ in a magnetic field coupled to a set of bosons is shown to be exactly equal to that of a one-dimensional gas and also, in a delicate limit, to that of a one-dimensional Ising model. Both of these are peculiar in that they must provide a free energy which is an intensive quantity. For special values of the parameters in the Hamiltonian, the partition function is equal to that first derived by Anderson and Yuval, and by Hamann, for the Kondo problem.