Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulae which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self-dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually-dual lattices. The examples include the ±J and Gaussian Ising spin glasses on the square, hexagonal and trianplar lattices, the Potts and Z _q models with chiral randomness on these lattices, and the three-dimensional ±J Ising spin glass and the random plaquette gauge model.