scholarly journals Off-equilibrium response function in the one-dimensional random-field Ising model

2002 ◽  
Vol 65 (4) ◽  
Author(s):  
F. Corberi ◽  
A. de Candia ◽  
E. Lippiello ◽  
M. Zannetti
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Response Function ◽  
Random Field Ising Model ◽  
One Dimensional ◽  
Equilibrium Response ◽  
The One

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.

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