Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model

Calabrese, P. and Caselle, M. and Celi, A. and Pelissetto, A. and Vicari, E. (2000) Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model. Journal of Physics A: Mathematical and General . ISSN 1361-6447

Abstract

We discuss the analytic properties of the Callan-Symanzik beta-function beta(g) associated with the zero-momentum four-point coupling g in the two-dimensional phi^4 model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behavior of beta(g) at the fixed point g^*. We argue that beta'(g) = beta'(g^*) + O(|g-g^*|^{1/7}) for N=1 and beta'(g) = beta'(g^*) + O(1/\log |g-g^*|) for N > 2. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi^4 theory. We discuss how these nonanalytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.

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