Mean field andε-expansion study of spin glasses

A Landau-Ginzburg phenomenological free energy for the Edwards and Anderson spin-glass model when there is competition between spin-glass and ferromagnetic ordering is developed. This free energy obtained with the use of the n→0 replication procedure is analyzed using mean-field theory and the ε expansion. Critical exponents for the ferromagnetic-spin-glass multicritical point are calculated in 6-ε dimensions. For Ising systems, ν=1/2+(2/3)ε and φ=1+(1/2)ε. For XY and Heisenberg systems, these exponents are complex. This result is not fully understood. The Harris-Plischke-Zuckermann model for amorphous magnetism is shown to have an Ising-like spin-glass fixed point in high enough dimension.