%0 Journal Article %1 Shukla2003DRIVEN %A Shukla, Prabodh %D 2003 %I World Scientific Publishing Co. %J Int. J. Mod. Phys. B %K bethe\_lattice, kinetics, critical-phenomena tree-graphs ising-model %N 29 %P 5583--5595 %R 10.1142/s0217979203023276 %T DRIVEN RANDOM FIELD ISING MODEL: SOME EXACTLY SOLVED EXAMPLES IN THRESHOLD ACTIVATED KINETICS %U http://arxiv.org/abs/cond-mat/0401252 %V 17 %X 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.

@article{Shukla2003DRIVEN, abstract = {{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.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Shukla, Prabodh}, biburl = {https://www.bibsonomy.org/bibtex/25172739a29b5c895375cf65f65bf7a42/nonancourt}, citeulike-article-id = {13052434}, citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0401252}, citeulike-linkout-1 = {http://dx.doi.org/10.1142/s0217979203023276}, citeulike-linkout-2 = {http://www.worldscientific.com/doi/abs/10.1142/S0217979203023276}, day = 20, doi = {10.1142/s0217979203023276}, eprint = {cond-mat/0401252}, interhash = {55eb28a30df22187edd28e9cd1e88a9d}, intrahash = {5172739a29b5c895375cf65f65bf7a42}, journal = {Int. J. Mod. Phys. B}, keywords = {bethe\_lattice, kinetics, critical-phenomena tree-graphs ising-model}, month = nov, number = 29, pages = {5583--5595}, posted-at = {2014-02-18 10:55:22}, priority = {2}, publisher = {World Scientific Publishing Co.}, timestamp = {2019-08-01T16:15:00.000+0200}, title = {DRIVEN RANDOM FIELD ISING MODEL: SOME EXACTLY SOLVED EXAMPLES IN THRESHOLD ACTIVATED KINETICS}, url = {http://arxiv.org/abs/cond-mat/0401252}, volume = 17, year = 2003 }