Dimensional Crossover in the Large N Limit

Details Dimensional Crossover in the Large N Limit Dimensional Crossover in the Large N Limit

1996-01-30

arxiv.org/abs/cond-mat/9601146v1

Physics

Condensed Matter

25 pages of PlainTex

Scientific paper

10.1007/BF02181488

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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