The non-perturbative renormalization group in the ordered phase

Details The non-perturbative renormalization group in the ordered phase The non-perturbative renormalization group in the ordered phase

2011-09-19

arxiv.org/abs/1109.4024v2

Nuclear Physics, Section B 855 (2012), pp. 854-884

Physics

Condensed Matter

Statistical Mechanics

27 pages, 14 figures, 7 tables

Scientific paper

10.1016/j.nuclphysb.2011.10.026

We study some analytical properties of the solutions of the non perturbative renormalization group flow equations for a scalar field theory with $Z_2$ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility $\chi(M)$ at $M=\pm M_0$ ($M_0$ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we stress that these conditions are not satisfied by a sharp cut-off in dimensions of space $d<4$.

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