scholarly journals A largeNphase transition in the continuum two dimensional SU(N) × SU(N) principal chiral model

2008 ◽  
Vol 2008 (04) ◽  
pp. 094-094 ◽  
Author(s):  
R Narayanan ◽  
H Neuberger ◽  
E Vicari
Keyword(s):  
Chiral Model ◽  
Two Dimensional ◽  
Principal Chiral Model ◽  
The Continuum

scholarly journals QUANTUM MECHANICALLY INDUCED WESS–ZUMINO TERM IN THE PRINCIPAL CHIRAL MODEL

1998 ◽  
Vol 13 (37) ◽  
pp. 3017-3024 ◽  
Author(s):  
HITOSHI MIYAZAKI ◽  
IZUMI TSUTSUI
Keyword(s):  
Configuration Space ◽  
Critical Value ◽  
Chiral Model ◽  
Quantum Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Dirac Monopole ◽  
Principal Chiral Model

It is argued that in the two-dimensional principal chiral model, the Wess–Zumino term may be induced quantum mechanically in a manner analogous to the θ-term in QCD. Our argument is based on the fact that the configuration space of the model has a structure topologically identified as a sphere, and that the Dirac monopole potential, which is induced on the sphere by inequivalent quantizations, appears in the guise of the Wess–Zumino term. Our result suggests that, at the critical value λ2=8π/|k| of the coupling constant, the principal chiral model belongs to the same family of models with the Wess–Zumino–Novikov–Witten model at the quantum level.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Sign in / Sign up

Export Citation Format

Share Document