Abstract

O' CONNOR, Denjoe; STEPHENS, C. R.  and  SANTIAGO, J. A.. Dimensional crossover in the non-linear sigma model. Rev. mex. fis. [online]. 2002, vol.48, n.4, pp.300-306. ISSN 0035-001X.

We consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the σ-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 δ_eff and β_eff that interpolate between their characteristic fixed point values associated with a d and (d - 1)-dimensional system in the limits T - T_c(L), with L(T - T_c(L))^v → ∞, and T - T_c(L) for L fixed respectively, where T_c(L) is the L-dependent critical temperature of the system.

Keywords : Renormalization group; dimensional crossover; critical phenomena; non-linear σ-model.

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