James P. Sethna: Research 1990 - 1994

In this past five years, I've been mostly interested in the dynamics of large interacting systems, with and without disorder. I've gradually moved from glassy systems without intrinsic disorder, through the dynamics of disordered systems undergoing martensitic transformations, and am now making progress on understanding the dynamics of hysteresis loops and void formation in electromigration. I've also always had a compelling interest in understanding data and fixing problems: my colleagues have led me into many fascinating problems over the past few years.

Immersed in a rich scientific environment, I've been drawn into several other projects through collaborations and conversations with my colleagues; I've grouped these into two broad categories. In addition, there are three topics on which my students and I have made substantial progress: slow relaxation, tweed in martensites, and hysteresis.

I. Talking with Experimentalists

Grappling with the real world is not only our job, but is also the source of our inspiration.
  1. Quasiparticle Bound States at a Superconducting Vortex Line: Harald Hess's Zero-Bias Tunneling Peak. (Shore, Huang, Dorsey; 41)
  2. Level Repulsion and Inhomogeneous Broadening: Ambrose and Sievers Find a Cusp. (52)
  3. Finite-Size Fluctuations in Sliding Charge-Density Waves: Rob Thorne's Skepticism Is Vindicated. (Myers; 63, 64)
  4. Void Dynamics and Electromigration: Moeckly and Buhrman's High-T_c River Deltas. (Wickham; 74)
  5. Null Results: Our Model for Bodenschatz's Defect Chaos Doesn't Correlate. (Roberts; 72)

II. Talking with Theorists

  1. Crack Growth Laws from Symmetry: Wash, Ingraffea, and Desert Floral Foam.(Hodgdon; 57)
  2. Negative Specific Heat: The Danes Melt a Copper Cluster. (65)
  3. Atomic Tunneling from a STM/AFM Tip: Mark Stiles' Phonons give an Ohmic Coupling.(Louis; 73)

III. Slow Relaxation

Several years ago, I spent a few months with Joel Shore and Ming Huang months working out some of Daniel Fisher's ideas on a scaling theory for the glass transition. Barrier heights were supposed to diverge as the ``ideal glass transition'' temperature $T_0$ was approached, and the resulting slowdown of the dynamics led to the diverging viscosities characteristic of glass formers. Abstract thought proving inadequate, Joel and I started trying to find a tangible model system for studying diverging barrier heights, and Shelly Shumway and I started thinking about ways to accelerate more traditional glass simulations.
  1. Logarithmic Growth in a Quenched Ising Model. (Shore, Holzer; 50, 55, 59)
  2. Evolving Enzymes: Accelerating Relaxation in Glassy Systems. (Shumway; 51, 54)
Despite this promising beginning, when students graduate their projects usually leave with them. I got dragged into some other directions, which frankly were more fun...

IV. Tweed in Martensites: a New Spin Glass (Kartha, Krumhansl; 56, 60, 70)

The field of disordered systems is predicated on the assumption that by studying some obscure, technologically irrelevant systems (spin glasses, charge-density waves, ...) we can find general principles which will apply to practical problems. I like our work on tweed, because we've mapped a practical problem in technologically important shape-memory alloys into the least likely of theoretical models: the infinite-range spin-glass, known and loved by practitioners of the black art of replica symmetry breaking.
  1. What is Tweed?.
  2. Tweed is a Spin Glass.

V. Hysteresis and Hierarchies: Dynamics of Disorder-Driven First-Order Phase Transformations (Dahmen, Perkovic'; 66, 68, 69, 75)

Even though everything is made of atoms that are 10^{-8} cm and wiggle at 10^{13} Hz, interesting things still happen on human length and time scales. Nineteenth century physics mastered hydrodynamics and elastic theory - describing systems where the fluctuations and the discreteness don't impinge on the behavior. In the seventies and the eighties, we mastered critical phenomena in equilibrium systems: near a continuous phase transition, the rapid fluctuations on the micro-scale propagate upward to human length and time scales, if one is near the critical temperature. Much attention has been focused in recent times on systems where the dynamics has events on all length and time scales: crackling noises, avalanches, earthquakes, ... We have been working on a class of models exhibiting hysteresis, where avalanches occur on large scales because we are in the neighborhood of a critical point. We're trying to blame avalanches on plain old criticality.
  1. The Return-Point Memory Effect, or Wiping Out.
  2. The Critical Point.
  3. The Epsilon Expansion.

Links Back

Entertaining Science done at
LASSP.
Last modified: January 15, 1995

James P. Sethna, sethna@lassp.cornell.edu

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).