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• W2079783224 startingPage "6202" @default.
• W2079783224 abstract "We develop a continuum path-integral approach for the ferroelectric five-vertex model in arbitrary d dimensions by mapping it to a directed polymer problem. A renormalization-group approach with an ensuremath{epsilon}=3-d expansion, 3 being the upper critical dimension, is used to study the polymer solution. The free-energy change due to the interaction of the chains has been computed to O(ensuremath{epsilon}), and the exact expression for the second virial coefficient has been obtained. The fixed point of the problem is found to be exactly 2ensuremath{pi}ensuremath{epsilon}. By use of finite-size-scaling theory and thermodynamics, the exponents for the vertex model are obtained from those of the polymeric system as the specific-heat exponent ensuremath{alpha}=(3-d)/2, and the incommensuration exponent ensuremath{beta}ifmmodebarelsetextasciimacronfi{}=(d-1)/2. The model is anisotropic with two length-scale exponents ${ensuremath{nu}}_{mathrm{?}}$=1 in one direction and ${ensuremath{nu}}_{mathrm{ensuremath{perp}}}$ =1/2 in the remaining d-1 directions. It is shown that there are no anomalous dimensions so that the exponents we obtain are exact." @default.
• W2079783224 created "2016-06-24" @default.
• W2079783224 creator A5016342313 @default.
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• W2079783224 date "1991-11-01" @default.
• W2079783224 modified "2023-09-23" @default.
• W2079783224 title "Absence of anomalous dimension in vertex models: Semidilute solution of directed polymers" @default.
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• W2079783224 doi "https://doi.org/10.1103/physreva.44.6202" @default.
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