Study on boundary–boundary correlation functions in the transverse Ising chain and chain

✍ Scribed by Asuka Sugiyama; Hidenori Suzuki; Masuo Suzuki

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 276 KB
• Volume: 353
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.01.028

✦ Synopsis

The topological interaction method proposed by Suzuki is applied to the transverse Ising chain and XY chain in order to study the behaviour of the boundary-boundary correlations. The correlation function hs x 1 s x N i for the thermodynamic limit is derived by this method as a function of the topological interaction parameter J 2 for finite temperatures. This analysis of the correlation function clarifies the emergence of the long-range order as temperature goes to zero. At zero temperature, a more general spin chain can be analysed analytically for N ! 1 and numerically for finite N to obtain the following results. The correlation function hs x 1 s x N i shows various kinds of behaviour, namely, (a) monotonic, (b) non-monotonic or (c) globally non-monotonic with small oscillation, with respect to the system-size N, in different regions of the parameters. The function hs y 1 s y N i shows also the above behaviour (a), or shows (d) globally monotonic decay with small oscillation.