±J Ising model on Dice lattices

We report the main results on ground state properties for a ±J Ising model defined on a Dice lattice. The sublattice method is adapted to this non-Archimedean system. By means of combinatorics and probability analysis, weight functions are obtained allowing to calculate properties such as frustrated plaquette distribution, frustration length, energy per bond, and fractional content of unfrustrated bonds; these analytic expressions are presented as functions of x (concentration of ferromagnetic bonds). On the other hand, these parameters are also calculated by an exact numerical algorithm applied to a large number of samples of increasing size N (number of spin sites) and values of x in the range [0.0,1.0]. Analytical and numerical results tend to agree, which makes these two techniques complementary to each other. Finally, a comparison is made to results previously reported for Archimedean lattices: it is found that Dice lattice presents a hybrid behavior being close to lattices with coordination 4 as far as energy is concerned but closer to lattices with coordination 3 when looking at topological parameters.