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

Journal Article · Thu Oct 15 04:00:00 EDT 1981 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(81)90099-3· OSTI ID:5755678

Ogilvie, M C

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/sub p/-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.

• Research Organization: Department of Physics, Brown University, Providence, Rhode Island 02912
• DOE Contract Number: AC02-76ER03130
• OSTI ID: 5755678
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 136:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CORRELATION FUNCTIONS
CRYSTAL MODELS
DUALITY
FERMIONS
FIELD THEORIES
FUNCTIONS
ISING MODEL
LAGRANGIAN FUNCTION
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MINKOWSKI SPACE
QUANTUM FIELD THEORY
SPACE
SPIN WAVES
THIRRING MODEL
VORTICES