Scaling Theory of the Ordered Phase of Real Spin Glasses
Theoretical approaches to spin glasses can be divided into two main categories. The first approach envisages constructing the mean-field solution of (say) the Edwards-Anderson1(EA) Hamiltonian and then systematically expanding about it to describe the properties of three-dimensional spin glasses. Producing a mean-field theory is equivalent to solving the Sherrington-Kirkpatrick2 (SK) spin-glass model. This model is now well understood and the solution reveals a rich structure of many pure states related by an ultrametric topology3. Fig 1(a) shows the expected phase diagram in a field. The SK model is the infinite dimensional limit of the EA Hamiltonian. Recent studies by Kondor4 suggest that the ultrametric behaviour, de Almeida-Thouless (AT)5 line etc. will not exist below six dimensions. Thus, the program of expanding about the customary mean-field solution to obtain the properties of spin glasses whose dimensionality is less than six does not look promising.
KeywordsSpin Glass Heisenberg Ferromagnet Replica Symmetry Breaking Experimental Time Scale Ising Spin Glass
Unable to display preview. Download preview PDF.
- 4.I. Kondor: to be publishedGoogle Scholar
- 6.For a review of the scaling theory see A.J. Bray and M.A. Moore: in Heidelberg Colloquium on Glassy Dynamics, Lecture Notes in Physics, 275, (Springer Verlag 1987 )Google Scholar
- 12.A. J. Bray and M.A. Moore: J. Phys. C17, L469 (1984)Google Scholar
- 16.L. Sandlund, P. Svedlindh, P. Granbery, P. Nordblad and L. Lundgren, to be published.Google Scholar