| In this thesis, I study the random-field Ising model (RFIM) in both theoretical and applied perspectives. For theoretical interests, I compare the avalanche behavior in equilibrium and non-equilibrium and find an unexpected universality. The application part focuses on the reliability test of the DeltaH(M, Delta M) methodology, which has been used to measure microscopic properties of magnetic recording media. Based on RFIM, an interacting random hysteron model has been developed and used to systematically test the reliability of the DeltaH(M, DeltaM) methodology.;Avalanche behavior in response to slowly changing external conditions is ubiquitous in a remarkably wide variety of dynamical systems. When driven far from equilibrium, those systems display impulsive cascade of dynamic avalanches spanning a broad range of sizes. Independent of their microscopic details, many non-equilibrium systems have been shown to have exactly the same dynamic avalanche behavior on many scales. This fact is called universality. So far, non-equilibrium systems were believed to be completely different from equilibrium ones. However, here we show that the zero-temperature RFIM exhibits surprisingly similar avalanche behavior in equilibrium and out of equilibrium. This finding solves a highly controversial question, i.e. whether the equilibrium and non-equilibrium disorder-induced phase transitions of RFIM belong to the same universality class. Our finding also indicates that generally equilibrium systems and their non-equilibrium counterparts may have deep connections.;In state-of-the-art storage applications such as hard disk drives, the intrinsic switching field distribution of the media grains is one of the most crucial properties defining the recording quality. However, this piece of microscopic information is very hard to measure macroscopically, especially for the perpendicular recording media. Using the interacting random hysteron model, we have studied the reliability of the recently developed Delta H(M, DeltaM) method. We demonstrated that this method does have several advantages over comparable methods. First, it has a well-defined reliability range and it allows for self-consistency checks. Second, the presence of dipolar interactions in the range of typical recording media substantially enhances the reliability of this method. Third, it is robust even in the presence of randomness in exchange or magnetostatic coupling within the range of a typical recording media. |
