Statistically interacting quasiparticles in Ising chains

Abstract

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 -> infinity, 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.