Four-loop contributions to long-distance quantities in the two-dimensional nonlinear sigma-model on a square lattice: revised numerical estimates

Abstract

We give the correct analytic expression of a finite integral appearing in the four-loop computation of the renormalization-group functions for the two-dimensional nonlinear sigma-model on the square lattice with standard action, explaining the origin of a numerical discrepancy. We revise the numerical expressions of Caracciolo and Pelissetto for the perturbative corrections of the susceptibility and of the correlation length. For the values used in Monte Carlo simulations, N=3, 4, 8, the second perturbative correction coefficient of the correlation length varies by 3%, 4%, 3% respectively. Other quantities vary similarly.

2 pages, Revtex, no figures

References in corpus (2)

• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• Correction to four-loop RG functions in the two-dimensional lattice O(n) $\sigma$-model

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