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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.11147 |
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| _version_ | 1866911030880239616 |
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| author | Tarjus, Gilles Tissier, Matthieu Balog, Ivan |
| author_facet | Tarjus, Gilles Tissier, Matthieu Balog, Ivan |
| contents | 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 $d_{\rm DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+ε$ 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 $ε=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_{\rm DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $ε=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_{\rm DR}$ for the RFIM, which we find around $5.11\pm0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the breakdown of dimensional reduction and supersymmetry in random-field models Tarjus, Gilles Tissier, Matthieu Balog, Ivan Disordered Systems and Neural Networks High Energy Physics - Theory 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 $d_{\rm DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+ε$ 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 $ε=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_{\rm DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $ε=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_{\rm DR}$ for the RFIM, which we find around $5.11\pm0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme. |
| title | On the breakdown of dimensional reduction and supersymmetry in random-field models |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.11147 |