On logarithmic extensions of local scale-invariance
arXiv:1009.4139 · doi:10.1016/j.nuclphysb.2012.12.007
Abstract
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.
23 pages, Latex2e, 2 eps figures included, final form (now also includes discussion of KPZ equation)
References in corpus (40)
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Gravity duals for non-relativistic CFTs
- Galilean Conformal Algebras and AdS/CFT
- Growing interfaces uncover universal fluctuations behind scale invariance
- Directed percolation criticality in turbulent liquid crystals
- An exact solution for the KPZ equation with flat initial conditions
- Non-relativistic conformal symmetries and Newton-Cartan structures
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- The KPZ equation with flat initial condition and the directed polymer with one free end
- From Percolation to Logarithmic Conformal Field Theory
- Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
- Local scale-invariance and ageing in noisy systems
- The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
- Directed polymer near a hard wall and KPZ equation in the half-space
- Correlation functions in the non-relativistic AdS/CFT correspondence
- Logarithmic observables in critical percolation
- Phenomenology of ageing in the Kardar-Parisi-Zhang equation
- Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
- Superuniversality in phase-ordering disordered ferromagnets
- The puzzle of bulk conformal field theories at central charge c=0
- Aging in coarsening diluted ferromagnets
- Ageing phenomena without detailed balance: the contact process
- Slow relaxation and aging kinetics for the driven lattice gas
- Ageing in the critical contact process: a Monte Carlo study
- Non-relativistic AdS/CFT and Aging/Gravity Duality
- Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line
- Non-equilibrium relaxation and critical aging for driven Ising lattice gases
- Pair correlations in sandpile model: a check of logarithmic conformal field theory
- Real-Time Correlators and Non-Relativistic Holography
- Characterisation of non-equilibrium growth through global two-time quantities
- Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
- On the 3-point functions of Aging Dynamics and the AdS/CFT Correspondence
- Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
- Causality from dynamical symmetry: an example from local scale-invariance
- The Jarzynski Identity and the AdS/CFT Duality
- Aging Logarithmic Conformal Field Theory : a holographic view
- Numerical investigation of the aging of the Fully-Frustrated XY model
- Towards the Construction of Local Logarithmic Conformal Field Theories
- Logarithmic corrections in the aging of the fully-frustrated Ising model
- Aging and stationary properties of non-equilibrium symmetrical three-state models
Cited by in corpus (18)
- Spherical model of growing interfaces
- Dynamical symmetries and causality in non-equilibrium phase transitions
- Schrödinger symmetry: a historical review
- From dynamical scaling to local scale-invariance: a tutorial
- Dynamical universality classes of simple growth and lattice gas models
- On Holographic Realization of Logarithmic GCA
- Causality from dynamical symmetry: an example from local scale-invariance
- Dynamical universality of the contact process
- Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
- Non-local representations of the ageing algebra in higher dimensions
- Logarithmic Exotic Conformal Galilean Algebras
- Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
- Physical ageing and new representations of some Lie algebras of local scale-invariance
- Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
- Aging Logarithmic Conformal Field Theory : a holographic view
- Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1
- Physical ageing from generalised time-translation-invariance
- Aging Logarithmic Galilean Field Theories