Infinite-Spin Limit of the Quantum Heisenberg Model
- 1 June 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (6), 1000-1005
- https://doi.org/10.1063/1.1665664
Abstract
The canonical partition function Q(H, N, s) for a spin-s anisotropic Heisenberg model with N sites, in external magnetic field H, is examined in the limit s → ∞. The coupling coefficients and the magnetic moment per spin are taken to be inversely proportional to s2 and s, respectively. It is proved that lim lim s→∞s−NQ(H,N,s)=(2π)−NQ(H,N),where Q(H, N) is the partition function for a corresponding classical Heisenberg model with spins of unit magnitude. This theorem makes precise the widely believed, but heretofore unproved equivalence between the classical Heisenberg model and the infinite-spin limit of the quantum Heisenberg model. No appeal to the thermodynamic limit is necessary.This publication has 18 references indexed in Scilit:
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