Title: Glass Phenomenology from the connection to spin glasses: review and ideas
1 Glass Phenomenology from the connection to spin glasses review and ideas
2 Conclusions (Moore)
Mapping between glass to spin glass in a magnetic field
Magnetic field corresponds to non-linearities. 3 Conclusions continued (Moore)
This mapping qualitatively accounts for
(1) Seemingly divergent time scales (VFT)
(2) Kauzmann crisis
(3) stretched exponential
(4) Increasing length scale
4 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.
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
6 One dimensional Edwards Anderson in a field
9 Ising spin glass in a field. Spin glass and divergent correlation length only in zero field. Spin glass transition is avoided for finite fields. 10 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.
11 Icosahedratics- coexisting local energetics (and avoided transition) and entropic droplet arguments.Ideal packing in a Lennard-Jones Liquid 12 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)) 13 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)) 14 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. 15 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! 16 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.
17 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. 18 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) 19 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).
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