A surprising physical interpretation of the replica number n was unveiled in the study of the equilibrium properties of the coupled dynamics of fast Ising spins and slow interactions: n is the ratio of the characteristic temperatures of the spin and the interaction systems and can take on any...

Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin glasses in finite dimensions, such as the exact energy, correlation identities and a functional relation between the distribution functions of ferromagnetic and spin glass order parameters. This last relation is useful...

We present a conjecture on the exact location of the multicritical point of models of spin glasses on the two-dimensional square lattice using duality transformation. The results not only agree very well with numerical estimates but also conform excellently to the existing knowledge on annealed...

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington–Kirkpatrick Ising spin glass with random...

A complete and exact characterization of the configuration space of 2-D ±J Ising lattices is performed. A new algorithm is introduced here representing advantages for reaching all states for small samples and doing a non-biased sampling of ground states for larger samples. We report efficient...