Dimensional Crossover in the Large N Limit

Abstract

We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover scaling forms for the free energy and the equation of state. We compare the results obtained using ``environmentally friendly'' renormalization with those found using a direct, non-renormalization group approach. A set of effective critical exponents are calculated and scaling laws for these exponents are shown to hold exactly, thereby yielding non-trivial relations between the various thermodynamic scaling functions.

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References in corpus (2)

• Environmentally Friendly Renormalization
• The Specific Heat of a Ferromagnetic Film.

Cited by in corpus (3)

• Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme
• Analysis of a continuous field theory in two dimensions with use of the Density Matrix Renormalization Group
• Ordering in magnetic films with surface anisotropy