Dimensional Crossover in the Non-Linear Sigma Model

Details Dimensional Crossover in the Non-Linear Sigma Model Dimensional Crossover in the Non-Linear Sigma Model

2002-02-12

arxiv.org/abs/cond-mat/0202209v1

Rev.Mex.Fis. 48 (2002) 300-306

Physics

Condensed Matter

Statistical Mechanics

12 pages, 4 postscript figures, to be published in Rev.Mex.Fis

Scientific paper

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.

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