Fluctuation effects in spin glasses

Abstract

This talk reviews recent work on the theory of spin glasses. The Edwards-Anderson approximation is explained and shown to be invalid even as a mean field theory because it predicts a certain positive definite correlation function to be negative. A method of restoring stability by breaking ’replica symmetry’ due to Bray and Moore is then discussed and shown to imply an infinite number of symmetry breakings in the ordered phase. Estimates of the ’lower critical dimension’ are reviewed. Several independent methods predict a value of four which, if correct, would imply that experiments have to be interpreted in terms of gradual freezing rather than a sharp phase transition. Finally we argue that the replica method gives correct results and previous difficulties arise from choosing an incorrect solution of the equations.