Delta Expansion on the Lattice and Dilated Scaling Region

Abstract

A new kind of delta expansion is applied on the lattice to the d=2 non-linear sigma model at N=infinity and N=1 which corresponds to the Ising model. We introduce the parameter delta for the dilation of the scaling region of the model with the replacement of the lattice spacing a to (1-delta)^{1/2}a. Then, we demonstrate that the expansion in delta admits an approximation of the scaling behavior of the model at both limits of N from the information at a large lattice spacing a.

arXiv comment11 pages, 18 figures

References in corpus (3)

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• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
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• Large-order aspects of the delta-expansion in low-dimensional Ising models
• Continuum Scaling from Large Mass Expansion on the Lattice: Delta Expansion Applied to the Anharmonic Oscillator
• Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice