Date of Original Version
The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s = 1/2, 1. In the s= 1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s = 1/2 and to a system of six species of soliton pairs for s = 1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain.
Ping Lu et al 2008 J. Phys. A: Math. Theor. 41 265003
Available at: http://dx.doi.org/10.1088/1751-8113/41/26/265003