Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-01-15
Int J Mod Phys B17, 5583(2003)
Physics
Condensed Matter
Statistical Mechanics
Invited talk at the Discussion Meeting on Statistical Mechanics of Threshold Activated Systems, IMSc, Chennai, India, (March,
Scientific paper
10.1142/S0217979203023276
The random field Ising model 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 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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