2003/11/20 by Prabodh Shukla · 6 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Ferromagnetism #Ising model #Lattice (music) #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum many-body systems #Random field #Spins #Square-lattice Ising model #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0217979203023276
published in International Journal of Modern Physics B 17(29), 5583-5595 (World Scientific) · Invited talk at the Discussion Meeting on Statistical Mechanics of Threshold Activated Systems, IMSc, Chennai, India, (March, 2003)
openalex publication_date 2003/11/20 · arxiv created 2004/01/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.