Glass Phenomenology from the connection to spin glasses: review and ideas

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Glass Phenomenology from the connection to spin
glasses review and ideas

• Nussinov
• Washington University

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Conclusions (Moore)

• Mapping between glass to spin glass in a magnetic
  field

Magnetic field corresponds to non-linearities.
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Conclusions continued (Moore)

• This mapping qualitatively accounts for
• (1) Seemingly divergent time scales (VFT)
• (2) Kauzmann crisis
• (3) stretched exponential
• (4) Increasing length scale

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More general idea/question

• Is there a general framework that includes
• spin-glass/RFOT (random field ferromagnet)
  /locally preferred structures (icosahedrics)/con
  strained dynamics/MCT/ many other approaches and
  facets as special cases?
• Defects as generalized spins (or other non spin
  type degrees of freedom in a spin glass type
  action)?
• RFOT on its own is remarkably potent and includes
  many ideas as subcases.

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Outline

• 1. Qualitative success of simplest spin glass
  model (one dimensional Edwards Anderson model
  with field) in accounting for seminal glass
  features
• (Tarzia and Moore)
• 2. Non-orthogonality of local structure
  approaches to RFOT (approaches complimentary)
• 3. Possible interpretation of spins as local
  defects.
• 4. General question based on symmetry grounds

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One dimensional Edwards Anderson in a field


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Ising spin glass in a field. Spin glass and
divergent correlation length only in zero field.
Spin glass transition is avoided for finite
fields.
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Microcrystalline order

• Several glass forming systems poised close to
  microcrystalline phases.
• E.g., several metallic glasses.
• Local structure as well as entropic
  considerations may be important.

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Icosahedratics- coexisting local energetics
(and avoided transition) and entropic droplet
arguments.Ideal packing in a Lennard-Jones Liquid
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We cannot keep going on forever

• The ideal packing can, however, be extended over
  a substantial volume if we consider the surface
  of a sphere embedded in d4 dimensions.
• By endowing space with curvature we may remove
  the 7 degree void.

(J. Sethna, Phys. Rev. Lett. 51, 2198 (1983))
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Landau-Ginzburg Expansion
The theory that of a system subjected to a
non-Abelian background (magnetic field) (S.
Sachdev D. R. Nelson, Phys. Rev. B 32,
4592(1985))
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An exponential number of metastable states in
the theory of icosahedral order
Z. Nussinov (cond-mat/0209292, PRB), G. Tarjus et
al. (cond-mat/0509127, JPCM)
Extensive configurational entropy
Glassy dynamics (Vogel-Fulcher)
Physical origin multitude of defect states
against backdrop of geometrically incompatible
locally preferred structures. Interaction between
defects.
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Unusual Equilibrium Thermodynamics Avoided Phase
Transitions in icosahedral theory
By performing a large n analysis (n169 complex
components in this theory) to second order in
1/n, deriving a generalized Mermin-Wagner
theorem, and performing a thermal fluctuation
analysis, we find that
Z. Nussinov (cond-mat/0209292, PRB), G. Tarjus et
al. (cond-mat/0509127, JPCM)
The thermodynamic phase transition is avoided!
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The generic phase diagram

• For any finite curvature, the system is hot.
• Why is there no phase transition?
• The huge degeneracy and near degeneracy of the
  system makes it very susceptible to thermal
  fluctuations.
• All of this is true for all non-abelian fields.
• Avoided transition due to field Similar to spin
  glass in field.

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Possible intuitive cause for spin glass
behavior Elastic strains generated by other
defects act on a given defect. If all motion is
nearly frozen then to compute the leading order
dynamics, we may regard the external defects as
quenched when computing the elastic interactions.
General long range interactions change phase.
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Defects spoiling locally preferred
structures Simplest defects Two level tunneling
systems/ Tunneling rotation impurities We can
envision defect modes against the backdrop of
preferred structures (e.g., P. Harrowells and
others). Integrating out phonons assuming
general crystalline like environment Schechter
and Stamp, arxiv0801.4944 obtained for two
level defects. Generalizations to tunneling
entities (Lubchenko and Wolynes)?
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Symmetry question for general quenched
theories Forget particular derivation. Most
general symmetry allowed Hamiltonian density
functional that breaks time reversal
Allows for paramagnetic, ferromagnetic, and spin
glass Phases. Includes replicas for quenched
quantities. When no long length scales/very low
frequency modes present, all degrees of freedom
must be present (as above).