1995/07/26 by Karin A. Dahmen, Karin Dahmen, James P. Sethna · 6 citations
Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed matter physics #Critical exponent #Exponent #Geometry #Hysteresis #Ising model #Material Dynamics and Properties #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Order (exchange) #Phase transition #Physics #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevb.53.14872
134 pages in REVTEX, plus 21 figures. The first two figures can be obtained from the references quoted in their respective figure captions, the remaining 19 figures are supplied separately in uuencoded format
arxiv created 1995/07/26 · openalex publication_date 1996/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Hysteresis loops are often seen in experiments at first-order phase transformations, when the system goes out of equilibrium. They may have a macroscopic jump (roughly as in the supercooling of liquids) or they may be smoothly varying (as seen in most magnets). We have studied the nonequilibrium zero-temperature random-field Ising-model as a model for hysteretic behavior at first-order phase transformations. As disorder is added, one finds a transition where the jump in the magnetization (corresponding to an infinite avalanche) decreases to zero. At this transition we find a diverging length scale, power-law distributions of noise (avalanches), and universal behavior. We expand the critical exponents about mean-field theory in 6-\ensuremathε dimensions. Using a mapping to the pure Ising model, we Borel sum the 6-\ensuremathε expansion to O(\mathrm\ensuremathε5) for the correlation length exponent. We have developed a method for directly calculating avalanche distribution exponents, which we perform to O(\ensuremathε). Our analytical predictions agree with numerical exponents in two, three, four, and five dimensions [Perkovi\ifmmode \acutec\else 'c\fi et al., Phys. Rev. Lett. 75, 4528 (1995)]. \textcopyright 1996 The American Physical Society.