A new method for the combinatorial optimization of quasi-one-dimensional systems is presented. This method is in close analogy with the well-known transfer-matrix method. The method allows for the calculation of the lowest energy levels of the system. However, when finding the ground and some...

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in...

We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey an ice rule. This augments some previous results which...

The diluted lattice formed by removing all exchange interactions that frustrate in the ground manifold of a ±J square Ising lattice is studied. The concentration of antiferromagnetic interactions, called x, is varied in the range [0.1,0.9]. Over 100000 samples 8×8 are solved at zero...