Abstract
We consider dimensional crossover for anO(N) Landau-Ginzburg-Wilson model on ad-dimensional film geometry of thicknessL 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 nontrivial relations between the various thermodynamic scaling functions.
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O'Connor, D., Stephens, C.R. & Bray, A.J. Dimensional crossover in the large-N limit. J Stat Phys 87, 273–291 (1997). https://doi.org/10.1007/BF02181488
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DOI: https://doi.org/10.1007/BF02181488