Dimensional Crossover in the Non-Linear Sigma Model
Statistical Mechanics
2007-05-23 v1 High Energy Physics - Theory
Abstract
We consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the sigma-model limit, using ``environmentally friendly'' renormalization. We show how to derive critical temperature shifts, giving explicit results to one loop. We also obtain expressions for the effective critical exponents delta and beta effective that interpolate between their characteristic fixed point values assocliated with a d and (d-1)-dimensional system in the limits T -> T_c(L), with L(T-T_c(L))^{\nu}->infty, and T->T_c(L) for L fixed respectively, where T_c(L) is the L-dependent critical temperature of the system.
Cite
@article{arxiv.cond-mat/0202209,
title = {Dimensional Crossover in the Non-Linear Sigma Model},
author = {Denjoe O'Connor and C. R. Stephens and J. A. Santiago},
journal= {arXiv preprint arXiv:cond-mat/0202209},
year = {2007}
}
Comments
12 pages, 4 postscript figures, to be published in Rev.Mex.Fis