Dimensional reduction and its breakdown in the 3-dimensional long-range random field Ising model

Abstract

We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the random-field Ising model in which both the interactions and the correlations of the disorder are long-ranged, i.e. power-law decaying. To some extent the power-law exponents play the role of spatial dimension in a short-range model, which allows us to probe the theoretically predicted existence of a nontrivial critical value separating a region where dimensional reduction holds from one where it is broken, while still considering the physical dimension d=3. By extending our recently developed approach based on a nonperturbative functional renormalization group combined with a supersymmetric formalism, we find that such a critical value indeed exists, provided one chooses a specific relation between the decay exponents of the interactions and of the disorder correlations. This transition from dimensional reduction to its breakdown should therefore be observable in simulations and numerical analyses, if not experimentally.

9 pages, 2 figures

References in corpus (29)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Optimisation of the exact renormalisation group
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Critical exponents from optimised renormalisation group flows
• Optimization of the derivative expansion in the nonperturbative renormalization group
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Mind The Gap
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media
• 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
• The Large Scale Energy Landscapes of Randomly Pinned Objects
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Universality in Three Dimensional Random-Field Ground States
• Creep via dynamical functional renormalization group
• 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
• First-principle derivation of static avalanche-size distribution
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Ground states and thermal states of the random field Ising model
• Ground state numerical study of the three-dimensional random field Ising model
• Critical exponents of four-dimensional random-field Ising systems
• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
• No-passing Rule in the Ground State Evolution of the Random-Field Ising Model

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• The nonperturbative functional renormalization group and its applications
• Criticality of Spin Systems with Weak Long-Range Interactions
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Anisotropic Long-Range Spin Systems
• Role of fluctuations in the yielding transition of two-dimensional glasses
• Critical behavior of the 2D Ising model with long-range correlated disorder
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• Critical behavior of the random-field Ising model with long-range interactions in one dimension
• Fixed points and their stability in the functional renormalization group of random field models
• Same universality class for the critical behavior in and out of equilibrium in a quenched random field
• Exact ground states of one-dimensional long-range random-field Ising magnets
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O($N$) spin model near lower critical dimension