Statistically interacting quasiparticles in Ising chains

Details Statistically interacting quasiparticles in Ising chains Statistically interacting quasiparticles in Ising chains

2007-10-09

arxiv.org/abs/0710.1687v1

Physics

Condensed Matter

Statistical Mechanics

18 pages and 4 figures

Scientific paper

10.1088/1751-8113/41/26/265003

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.

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