A consistent loop expansion around Parisi's replica symmetry breaking mean field theory for the Ising spin glass is constructed. Above the upper critical dimension d = 6 the short range corrections can be absorbed into the parameters of a Ginzburg-Landau type free energy functional whereby the d < ∞ dimensional theory can be mapped back onto mean field theory. For d > 8 the map is regular, thus mean field exponents are preserved, only prefactors are modified. For 6 < d < 8 the order parameter and the spectrum acquire non-trivial exponents which can still be calculated exactly. In the limit d →6 + 0 scaling is restored.
|Number of pages||10|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - Jun 15 1992|
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics