Relaxation time for a dimer covering with height representation
Abstract
This paper considers the Monte Carlo dynamics of random dimer coverings of the square lattice, which can be mapped to a rough interface model. Two kinds of slow modes are identified, associated respectively with long-wavelength fluctuations of the interface height, and with slow drift (in time) of the system-wide mean height. Within a continuum theory, the longest relaxation time for either kind of mode scales as the system size N. For the real, discrete model, an exact lower bound of O(N) is placed on the relaxation time, using variational eigenfunctions corresponding to the two kinds of continuum modes.
Keywords
Cite
@article{arxiv.cond-mat/9607222,
title = {Relaxation time for a dimer covering with height representation},
author = {C. L. Henley},
journal= {arXiv preprint arXiv:cond-mat/9607222},
year = {2009}
}
Comments
12 pages, LaTeX; 1 figure in PostScript file; to appear, J. Stat. Phys. Sections and subsections were reshuffled to improve presentation, some text added on quantum-dimer model, fully-frustrated Ising model, and application to general class of "height" models