The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Ground State Structure, Domain Walls, and External Field Response in Random Magnets

Eira Seppälä

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics, Helsinki University of Technology for public examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 25th of May, 2001, at 12 o'clock noon.

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Abstract

The ground state structure and domain walls in Ising-like magnets with quenched randomness are studied at zero temperature. The methods employed are exact ground state calculations using graph-theoretical optimization and extreme statistics arguments.

The elastic manifolds, i.e., domain walls, with random-bond disorder are investigated with two different types of periodicity. The first type of periodicity is when the randomness is periodically repeated. It is shown to lead after a cross-over to the periodic elastic media universality class, whenever the period lambda is finite. The second periodicity is due to an additional modulating potential. There are two types of intermittence seen before the asymptotic random-bond roughness behavior is reached. The first type is when the manifolds jump between the minima of the periodic potential and the second type is when the interfaces roughen over pinning energy barriers.

An external field is applied to the random manifolds. An energy minimization argument based on the glassy energy landscape indicates that in an equilibrium system the manifolds move by sharp jumps between nearly degenerate energy minima in analogy to a first-order transition. A mean field argument for the finite-size scaling of the first jump field is derived and numerically confirmed. Using extreme statistics and probabilistic arguments, the probability distribution of the first jump field and its finite size scaling are calculated. Based on these the susceptibility of the manifolds is derived.

Random field magnets are studied in two dimensions. The break-up of long-range order is shown to have a first-order character. The domain wall behavior is studied, leading to an interface scaling with a roughness exponent greater than unity below the break-up length scale. The domain wall energy is demonstrated to vanish logarithmically confirming the destruction of the long-range order. The magnetization and susceptibility versus the external field are investigated, and they show continuous behaviors and are independent of the break-up length scale. However, another long-range order, percolation, is found in two-dimensional random field magnets. The percolation transition with respect to the external field belongs to the standard short-range correlated two-dimensional percolation universality class. The whole phase diagram for percolation as a function of the random field strength and the external field is predicted.

This thesis consists of an overview and of the following 7 publications:

  1. E. T. Seppälä, M. J. Alava, and P. M. Duxbury, Periodic elastic medium in which periodicity is relevant, Physical Review E 62, 3230-3233 (2000). © 2000 American Physical Society. By permission.
  2. E. T. Seppälä, M. J. Alava, and P. M. Duxbury, Intermittence and roughening of periodic elastic media, Physical Review E 63, 036126 (2001) (7 pages). © 2001 American Physical Society. By permission.
  3. E. T. Seppälä and M. J. Alava, Energy landscapes in random systems, driven interfaces and wetting, Physical Review Letters 84, 3982-3985 (2000). © 2000 American Physical Society. By permission.
  4. E. T. Seppälä, M. J. Alava, and P. M. Duxbury, Extremal statistics in the energetics of domain walls, Physical Review E 63, 066110 (2001) (4 pages). © 2001 American Physical Society. By permission.
  5. E. T. Seppälä and M. J. Alava, Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature, accepted for publication in European Physical Journal B. © 2001 EDP Sciences. By permission.
  6. E. T. Seppälä, V. Petäjä, and M. J. Alava, Disorder, order, and domain wall roughening in the two-dimensional random field Ising model, Physical Review E 58, R5217-R5220 (1998). © 1998 American Physical Society. By permission.
  7. E. T. Seppälä and M. J. Alava, Susceptibility and percolation in two-dimensional random field Ising magnets, Physical Review E 63, 066109 (2001) (14 pages). © 2001 American Physical Society. By permission.

Keywords: quenched randomness, Ising model, domain walls, optimization, percolation

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© 2001 Helsinki University of Technology

Last update 2011-05-26