Physics – Condensed Matter
Scientific paper
1993-06-21
Physics
Condensed Matter
16 pages LaTeX, one of the 2 figures included as a postscript file. Oxford preprint OUTP-93-18S, to be published in Phys. Rev.
Scientific paper
10.1103/PhysRevB.48.7125
The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We discuss the global structure of the spectrum of Heisenberg models with arbitrary couplings, using group theoretical methods. The Hilbert space breaks up in blocks characterized by the quantum numbers of the total spin, $S$ and $M$, and each block is shown to constitute the representation space of an explicitly given irreducible representation of the symmetric group $S_N$, consisting of permutations of the $N$ spins in the system. In the second part of the paper we consider, as a concrete application, the model where each spin is coupled to all the other spins with equal strength. Its partition function is written as a single integral, elucidating its $N$-dependence. This provides a useful framework for studying finite size effects. We give explicit results for the heat capacity, revealing interesting behavior just around the phase transition.
No associations
LandOfFree
Heisenberg models and a particular isotropic model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Heisenberg models and a particular isotropic model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heisenberg models and a particular isotropic model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-326175