Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group

Abstract

We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead to the loss of dimensional reduction. This problem is reduced to studying the anomalous dimensions of "leaders" -- lowest dimension parts of $S_n$-invariant perturbations in the Cardy basis. Leader operators are classified as non-susy-writable, susy-writable or susy-null depending on their symmetry. Susy-writable leaders are additionally classified as belonging to superprimary multiplets transforming in particular $\text{OSp}(d|2)$ representations. We enumerate all leaders up to 6d dimension $\Delta =12$, and compute their perturbative anomalous dimensions (up to two loops). We thus identify two perturbations (with susy-null and non-susy-writable leaders) becoming relevant below a critical dimension $d_c\approx 4.2$ - $4.7$. This supports the scenario that the SUSY fixed point exists for all $3<d\le 6$, but becomes unstable for $d<d_c$.

arXiv comment103 pages, 15 figures. v2: susy-null leader discussion modified (Sec. 8.5 and App. A.6), and other tweaks. v3: version accepted by JHEP, added executive summary in Sec. 1.1, discussion in Sec 11.1.1 and Sec. 11.2.1, corrected typos. v4: corrected typos. Conclusions unchanged

References in corpus (61)

• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Precision Islands in the Ising and $O(N)$ Models
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Walking, Weak first-order transitions, and Complex CFTs
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Dijet Cross Sections and Parton Densities in Diffractive DIS at HERA
• More constraining conformal bootstrap
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Boundary and Interface CFTs from the Conformal Bootstrap
• A Cheap Alternative to the Lattice?
• Numbers and Functions in Quantum Field Theory
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Universality in the three-dimensional random-field Ising model
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• The Epsilon Expansion Meets Semiclassics
• The 3d Stress-Tensor Bootstrap
• Supersymmetry and its spontaneous breaking in the random field Ising model
• Conformal correlators of mixed-symmetry tensors
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• Simulations of lattice animals and trees
• Scale Invariance in disordered systems: the example of the Random Field Ising Model
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• The ABC (in any D) of Logarithmic CFT
• Spinning operators and defects in conformal field theory
• Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• New phenomena in the random field Ising model
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Tensor envelopes of regular categories
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• The spectrum of critical exponents in $({\vec{\varphi }}^2{)}^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures
• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• Identity of the universal repulsive-core singularity with Yang-Lee edge criticality
• Interactions of several replicas in the random field Ising model
• Critical slowing down in polynomial time algorithms
• Mixed Scalar-Current bootstrap in three dimensions
• The Spectrum of Yang Mills on a Sphere
• On the stability problem in the O(N) nonlinear sigma model
• A construction of semisimple tensor categories
• Charting the space of 3D CFTs with a continuous global symmetry
• Is the phase transition in the Heisenberg model described by the $(2+\epsilon )$-expansion of the nonlinear $\sigma$-model?
• Weighted Mean Field Theory for the Random Field Ising Model
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• High-gradient operators in the N-vector model
• A structural test for the conformal invariance of the critical 3d Ising model
• New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature
• Fixed points and their stability in the functional renormalization group of random field models
• (No) Bootstrap for the Fractal Ising Model
• Lecture on Branched Polymers and Dimensional Reduction
• Fancy and facts in the (d - 2) expansion of non-linear sigma models
• Renormalization group for the probability distribution of magnetic impurities in a random-field ${\varphi }^4$ model
• Comment on "Evidence for Supersymmetry in the Random-Field Ising Model at D=5''
• Dimensional reduction in supersymmetric field theories

Cited by in corpus (15)

• The fate of Parisi-Sourlas supersymmetry in Random Field models
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Renormalization group for measurement and entanglement phase transitions
• Finite-size scaling of the random-field Ising model above the upper critical dimension
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Ensemble averages, Poisson processes and Microstates
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Supersymmetries in non-equilibrium Langevin dynamics
• The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs
• Quenched random mass disorder in the large N theory of vector bosons
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Topological Field Theory and Stochastic Dynamics