Quantum field theory of Kosterlitz-Thouless phase transitions

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1980

OSTI ID:6144602

Ogilvie, M C

A general quantum field-theoretic formalism for the study of Kosterlitz-Thouless phase transition is developed and applied to several models. The structure of the free, massless scalar field is discussed, making explicit its connection with the Gaussian model. The close connection of the spin-wave and vortex operators with two-dimensional fermion-boson equivalences is stressed. The critical behavior of the planar model is reviewed, using field-theoretic methods applied to the sine-Gordon model. The Kosterlitz-Thouless phase transition in two-dimensional dislocation-mediated melting is studied using a vector generalization of the sine-Gordon model. Recent second-order renormalization group calculations are confirmed, and the issue of universal third-order corrections is discussed. It is shown that the Gross-Neveu model can be interpreted as a massive theory associated with a Kosterlitz-Thouless critical point. Finally, the Ising and Baxter models are studied using the methods developed here. It is shown that the vortex and spin-wave excitations in the Ising model conspire to produce a free, massive Majorana fermion field theory in the continuum limit. The formalism is then extended to the Baxter model. Recent results on the Baxter and Ashkin-Teller models are rederived and extended.

• Research Organization: Brown Univ., Providence, RI (USA)
• OSTI ID: 6144602
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CRYSTAL MODELS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
ISING MODEL
MATHEMATICAL MODELS
PHASE TRANSFORMATIONS
QUANTUM FIELD THEORY
SINE-GORDON EQUATION