Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group

Abstract

We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The approach solves some of the questions concerning the critical behavior of random-field systems that have stayed pending for many years: What is the mechanism for the breakdown of dimensional reduction and the breaking of the underlying supersymmetry below $d=6$? Can one provide a theoretical computation of the critical exponents, including the exponent ψcharacterizing the activated dynamic scaling? Is it possible to theoretically describe collective phenomena such as avalanches and droplets? Is the critical scaling described by 2 or 3 independent exponents? What is the phase behavior of the random-field $O(N)$ model in the whole ($N$, $d$) plane and what is the lower critical dimension of quasi-long range order for $N=2$? Are the equilibrium and out-of-equilibrium critical points of the RFIM in the same universality class?

arXiv commentReview submitted to the topical issue of EPJB on "Recent advances in the theory of disordered systems"; 19 pages, 7 figures

References in corpus (90)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Crackling Noise
• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Elastic theory of flux lattices in presence of weak disorder
• Creep and depinning in disordered media
• Elastic Theory of pinned flux lattices
• Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior
• A random critical point separates brittle and ductile yielding transitions in amorphous materials
• Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
• Moving glass phase of driven lattices
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• Renormalization of pinned elastic systems: how does it work beyond one loop ?
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Crises and collective socio-economic phenomena: simple models and challenges
• Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors
• Topological Defects in the Random-Field XY Model and Randomly Pinned Vortex Lattices
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Universality in the three-dimensional random-field Ising model
• Avalanche-size distribution at the depinning transition: A numerical test of the theory
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Field Theory of Fluctuations in Glasses
• On the athermal character of structural phase transitions
• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Supersymmetry and its spontaneous breaking in the random field Ising model
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach
• Finite Size Scaling analysis of the avalanches in the 3d Gaussian Random Field Ising Model with metastable dynamics
• Statistics of static avalanches in a random pinning landscape
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Scale Invariance in disordered systems: the example of the Random Field Ising Model
• Spanning avalanches in the three-dimensional Gaussian Random Field Ising Model with metastable dynamics: field dependence and geometrical properties
• Ferromagnet in a continuously tuneable random field
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors
• Elusive Glassy Phase in the Random Field Ising Model
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Random-field-like criticality in glass-forming liquids
• Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-εdimensions
• First-principle derivation of static avalanche-size distribution
• Quantum spin glass and the dipolar interaction
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Stability of Random-Field and Random-Anisotropy Fixed Points at large N
• Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Ground states and thermal states of the random field Ising model
• Random Field Driven Spatial Complexity at the Mott Transition in VO2
• Criticality of the random field Ising model in and out of equilibrium: a nonperturbative functional renormalization group description
• Unexpected universality in static and dynamic avalanches
• Numerical study of the random field Ising model at zero and positive temperature
• Constructing explicit magnetic analogies for the dynamics of glass forming liquids
• Universality Classes of Critical Points in Constrained Glasses
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets
• Absence of replica symmetry breaking in the random field Ising model
• Interactions of several replicas in the random field Ising model
• Fluctuating orders and quenched randomness in the cuprates
• No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model
• Random Field Ising Model In and Out of Equilibrium
• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Colloid-polymer mixtures in random porous media: Finite size scaling and connected versus disconnected susceptibilities
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• Activated dynamic scaling in the random-field Ising model: a nonperturbative functional renormalization group approach
• Evidence for a disorder driven phase transition in the condensation of 4He in aerogels
• Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid
• No-passing Rule in the Ground State Evolution of the Random-Field Ising Model
• Critical behavior of the random-field Ising model with long-range interactions in one dimension
• Dimensional reduction and its breakdown in the 3-dimensional long-range random field Ising model
• Stability of fixed points in the (4+ε)-dimensional random field O(N) spin model for sufficiently large N
• Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
• Fixed points and their stability in the functional renormalization group of random field models
• Maximal Mean Field Solutions in the Random Field Ising Model: the Pattern of the Symmetry Breaking
• Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
• The random anisotropy model revisited
• Hierarchical Reference Theory of critical fluids in disordered porous media
• Low-energy excitations in the three-dimensional random-field Ising model
• Functionality of disorder in muscle mechanics
• Direct Measurement of Random Fields in the $LiH{o}_x{Y}_{1-x}{F}_4$ Crystal
• Dimensional reduction and its breakdown in the driven random field O(N) model
• Comment on ``Random-Field Spin Model beyond 1 Loop: A Mechanism for Decreasing the Lower Critical Dimension"
• Comment on "Evidence for Supersymmetry in the Random-Field Ising Model at D=5''

Cited by in corpus (28)

• The nonperturbative functional renormalization group and its applications
• Statistical mechanics of coupled supercooled liquids in finite dimensions
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Mott-glass phase of a one-dimensional quantum fluid with long-range interactions
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Chaos in the Bose-glass phase of a one-dimensional disordered Bose fluid
• Domain Growth and Aging in the Random Field XY Model: A Monte Carlo Study
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Thermal vestiges of avalanches in the driven random field Ising model
• Wrinkling transition in quenched disordered membranes at two loops
• Dimensional reduction breakdown and correction to scaling in the random-field Ising model
• Supersymmetries in non-equilibrium Langevin dynamics
• Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension
• Critical behaviours of anisotropic XY ferromagnet in the presence of random field
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• Energy minima and ordering in ferromagnets with quenched randomness
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions
• Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions
• Interplay of Quantum and Thermal Fluctuations in Two-Dimensional Randomly Pinned Charge Density Waves
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes
• Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Renormalization group approach to the elastic properties of graphene bilayers
• The Schwartz-Soffer and more inequalities for random fields
• Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$