TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.001
TI  - On the breakdown of dimensional reduction and supersymmetry in random-field models
PY  - 2025/07/01
UR  - https://scipost.org/SciPostPhys.19.1.001
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 001
A1  - Tarjus, Gilles
AU  - Tissier, Matthieu
AU  - Balog, Ivan
AB  - We discuss the breakdown of the Parisi-Sourlas supersymmetry (SUSY) and of the dimensional-reduction (DR) property in the random field Ising and O($N$) models as a function of space dimension $d$ and/or number of components $N$. The functional renormalization group (FRG) predicts that this takes place below a critical line $d_\mathrm{DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+\epsilon$ and carry out a more comprehensive investigation of the nonperturbative FRG approximation for the RFIM. In light of this FRG description, we discuss the perturbative results in $\epsilon=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_\mathrm{DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $\epsilon=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_\mathrm{DR}$ for the RFIM, which we find around $5.11±0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme.
ER  -

@Article{10.21468/SciPostPhys.19.1.001,
	title={{On the breakdown of dimensional reduction and supersymmetry in random-field models}},
	author={Gilles Tarjus and Matthieu Tissier and Ivan Balog},
	journal={SciPost Phys.},
	volume={19},
	pages={001},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.001},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.001},
}