Numerical results on a hypercubic cell spin glass model

The authors study a spin glass hypercubic cell in D dimensions (i.e. hypercubic lattice with L=2 where L is the lattice size) for different values of D by means of Monte Carlo simulation. In the limit D to infinity this model converges to the SK model as well as for hypercubic lattices. They confirm the usual interpretation of the spin glass phase. Since this model is more similar to hypercubic lattices than to the infinite-range model these results suggest that broken replica symmetry is useful to study finite-dimensional hypercubic lattices above a certain critical dimension.