scholarly journals The non-equilibrium response of the critical Ising model: universal scaling properties and local scale invariance

2008 ◽  
Vol 2008 (02) ◽  
pp. P02013 ◽  
Author(s):  
Federico Corberi ◽  
Andrea Gambassi ◽  
Eugenio Lippiello ◽  
Marco Zannetti
Keyword(s):  
Ising Model ◽  
Scale Invariance ◽  
Local Scale ◽  
Scaling Properties ◽  
Universal Scaling ◽  
Equilibrium Response ◽  
Non Equilibrium

scholarly journals DRIVEN RANDOM FIELD ISING MODEL: SOME EXACTLY SOLVED EXAMPLES IN THRESHOLD ACTIVATED KINETICS

2003 ◽  
Vol 17 (29) ◽  
pp. 5583-5595 ◽  
Author(s):  
PRABODH SHUKLA
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Probabilistic Method ◽  
Bethe Lattice ◽  
Initial State ◽  
Random Field Ising Model ◽  
Theoretical Approaches ◽  
Equilibrium Response ◽  
Ferromagnetic Interactions ◽  
Non Equilibrium

The random field Ising Model (RFIM) driven by a slowly varying uniform external field at zero temperature provides a caricature of several threshold activated systems. In this model, the non-equilibrium response of the system can be obtained analytically in one dimension as well as on a Bethe lattice if the initial state of the system has all spins aligned parallel to each other. We consider ferromagnetic as well as anti-ferromagnetic interactions. The ferromagnetic model exhibits avalanches and non-equilibrium critical behavior. The anti-ferromagnetic model is marked by the absence of these features. The ferromagnetic model is Abelian, and the anti-ferromagnetic model is non-Abelian. Theoretical approaches based on the probabilistic method are discussed in the two cases, and illustrated by deriving some basic results.

scholarly journals Lifshitz hydrodynamics at generic z from a moving black brane

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Aruna Rajagopal ◽  
Larus Thorlacius
Keyword(s):  
Field Theory ◽  
Steady State ◽  
Critical Exponent ◽  
Stress Tensor ◽  
Perfect Fluid ◽  
Scale Invariance ◽  
Linear Momentum ◽  
Black Brane ◽  
Dilaton Gravity ◽  
Non Equilibrium

Abstract A Lifshitz black brane at generic dynamical critical exponent z > 1, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.

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