On the breakdown of dimensional reduction and supersymmetry in random-field models

Abstract

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 $5.11\pm 0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme.

29 pages, 6 figures, 7 appendices. Submitted to SciPost Physics

References in corpus (13)

• Exact evolution equation for the effective potential
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Numerical study of the random field Ising model at zero and positive temperature
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• The fate of Parisi-Sourlas supersymmetry in Random Field models
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• No-passing Rule in the Ground State Evolution of the Random-Field Ising Model
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Stability of fixed points in the (4+ε)-dimensional random field O(N) spin model for sufficiently large N
• Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction
• Dimensional reduction breakdown and correction to scaling in the random-field Ising model
• Comment on ``Random-Field Spin Model beyond 1 Loop: A Mechanism for Decreasing the Lower Critical Dimension"
• The random free field scalar theory

Cited by in corpus (1)

• Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective