Spin waves, vortices, fermions, and duality in the Ising and Baxter models

✍ Scribed by Michael C Ogilvie

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 890 KB
• Volume: 136
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(81)90099-3

✦ Synopsis

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition. that the Z, Villain models are related to a class of continuum field theories with analogous duality properties.

Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.