KBD algorithm

The KBD algorithm is a cluster update algorithm designed for the fully frustrated Ising model in two dimensions, or more generally any two dimensional spin glass with frustrated plaquettes arranged in a checkered pattern. It is discovered in 1990 by Daniel Kandel, Radel Ben-Av, and Eytan Domany, and generalized by P. D. Coddington and L. Han in 1994. It is the inspiration for cluster algorithms used in quantum monte carlo simulations.

Furthermore, it can be shown that there must be at least two such cycles, and that the cycles cannot intersect. Most importantly, each cycle cannot be contracted to a point in the underlying surface that the lattice is embedded in. On a periodic lattice (or a torus), this means that the cycles of closed bonds must wind around the torus in the same direction, from which one can show that the largest cluster (which must be "squeezed" between these cycles) at zero temperature cannot span a finite fraction of the lattice size in the thermodynamic limit.