The Large N Random Phase sine-Gordon Model

Abstract

At large distances and in the low temperature phase, the quenched correlation functions in the 2d random phase sine-Gordon model have been argued to be of the form~: $ \bar {\vev{~[φ(x)-φ(0)]^2~}}_* = A (\log|x|) + B \ep^2 (\log|x|)^2 $, with $\ep=(T-T_c)$. However, renormalization group computations predict $B\ne 0$ while variational approaches (which are supposed to be exact for models with a large number of components) give $B=0$. We introduce a large $N$ version of the random phase sine-Gordon model. Using non-Abelian bosonization and renormalization group techniques, we show that the correlation functions of our models have the above form but with a coefficient $B$ suppressed by a factor $1/N^3$ compared to $A$.

8 pages, plain latex, no figures

References in corpus (5)

• Elastic Theory of pinned flux lattices
• Replica Symmetry Breaking Instability in the 2D XY model in a random field
• Dynamic and Static Properties of the Randomly Pinned Planar Flux Array
• Glassy Roughness of a Crystalline Surface Upon a Disordered Substrate
• Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array

Cited by in corpus (4)

• Glass phase of two-dimensional triangular elastic lattices with disorder
• Exact form of the exponential correlation function in the glassy super-rough phase
• New evidence for super-roughening in crystalline surfaces with disordered substrate
• Numerical Simulations of Random Phase Sine-Gordon Model and Renormalization Group Predictions