Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
arXiv:1808.02767 · doi:10.1103/PhysRevE.99.022132
Abstract
A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point/limit cycle may thus stay finite for all dimensions.
arXiv comment5+8 pages, 3 figures. arXiv admin note: text overlap with arXiv:1607.04217
References in corpus (45)
- Exact evolution equation for the effective potential
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- The many-body localization phase transition
- The Exact Renormalisation Group and Approximate Solutions
- Bounding scalar operator dimensions in 4D CFT
- Solving the 3D Ising Model with the Conformal Bootstrap
- Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
- Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
- Discrete scale invariance and complex dimensions
- Fractal free energy landscapes in structural glasses
- Stock market crashes, Precursors and Replicas
- An Introduction to the Nonperturbative Renormalization Group
- Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
- More constraining conformal bootstrap
- Growing timescales and lengthscales characterizing vibrations of amorphous solids
- Breakdown of Elasticity in Amorphous Solids
- Following the evolution of glassy states under external perturbations: compression and shear-strain
- Ordering and Broken Symmetry in Short-Ranged Spin Glasses
- 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
- Experimental evidences of the Gardner phase in a granular glass
- A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
- Disappearance of the de Almeida-Thouless line in six dimensions
- Two loop results from one loop computations and non perturbative solutions of exact evolution equations
- Exploring the complex free energy landscape of the simplest glass by rheology
- Absence of Marginal Stability in a Structural Glass
- Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
- Thermodynamic glass transition in a spin glass without time-reversal symmetry
- Johari-Goldstein relaxation far below Tg: Experimental evidence for the Gardner transition in structural glasses?
- Replica symmetry breaking in and around six dimensions
- Nontrivial critical fixed point for replica-symmetry-breaking transitions
- Spin glass transition in a magnetic field: a renormalization group study
- Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
- Spin-glass--like aging in colloidal and granular glasses
- Glassy, Gardner-like Phenomenology in Minimally Polydisperse Crystalline Systems
- Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers
- Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
- The Gardner transition in finite dimensions
- Real Space Renormalization Group Theory of Disordered Models of Glasses
- Exact renormalization group equation for the Lifshitz critical point
- Multicritical point on the de Almeida-Thouless line in spin glasses in dimensions
- Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
- Comment on "Critical point scaling of Ising spin glasses in a magnetic field" by J. Yeo and M.A. Moore
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- Perspective: Gardner Physics in Amorphous Solids and Beyond
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- Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
- Impact of jamming criticality on low-temperature anomalies in structural glasses
- Dynamical coexistence in moderately polydisperse hard-sphere glasses
- Spin-glass dynamics: experiment, theory and simulation
- Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
- Bethe -layer construction on the Ising model
- Critical exponents of the spin glass transition in a field at zero temperature
- Evidence of de Almeida-Thouless line below six dimensions
- Long-range spin glass in a field at zero temperature