8 January, 2010
Spin glasses and density functional theory
Lecture 2: Density functional thoery
Abstract
In these lectures, I will provide an introduction to theoretical concepts and techniques developed in studies of spin glasses [1] and discuss applications of these concepts and methods of calculation in attempts to understand the behavior of supercooled liquids near the structural glass transition. I will alsoprovide an introduction to the density functional theory [2] of inhomogeneous liquids that provides a natural way of relating spin glasses to structural glasses.
Topics to be covered in these lectures include:
1. The Sherrington-Kirkpatrick (SK) model and the Thouless-Anderson-Palmer (TAP) equations.
2. The replica formalism, replica symmetry breaking and the Parisi solution for the SK model.
3. Spin glass models [3] that exhibit random first-order transitions [4].
4. Classical density functional theory of inhomogeneous liquids and its application [5,6] in studies of supercooled liquids and the glass transition.
References and suggested reading
- K. Binder and A. P Young, Rev. Mod. Phys. 58, 801 (1986)
- Y. Singh, Phys. Rep. 207, 351 (1991)
- T. R. Kirkpatrick, D. Thirumalai and P. G. Wolynes, Phys. Rev. A 40, 1045 (1989), and references therein
- V. Lubchenko and P. G. Wolynes, Annu. Rev. Phys. Chem. 58, 235 (2007) http://arxiv.org/abs/cond-mat/0607349
- Y. Singh, J.P. Stoessel, and P.G. Wolynes, Phys. Rev. Lett. 54, 1059 (1985)
- P. Chaudhury, S. Karmakar and C. Dasgupta, Phys. Rev. Lett. 100, 125701 (2008), and references therein