Ising lattices with ±J second-nearest-neighbor interactions.

A. J. RAMIREZ-PASTOR; F. NIETO; E. E. VOGEL

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

Año: 1997 vol. 55 p. 14323 - 14329

0163-1829

Second-nearest-neighbor interactions are added to the usual nearest-neighbor Ising Hamiltonian for square lattices in different ways. The starting point is a square lattice where half the nearest-neighbor interactions are ferromagnetic and the other half of the bonds are antiferromagnetic. Then, second-nearest-neighbor interactions can also be assigned randomly or in a variety of causal manners determined by the nearest-neighbor interactions. In the present paper we consider three causal and three random ways of assigning second-nearestneighbor exchange interactions. Several ground-state properties are then calculated for each of these lattices: energy per bond e g , site correlation parameter pg , maximal magnetization mg , and fraction of unfrustrated bonds hg . A set of 500 samples is considered for each size N ~number of spins! and array ~way of distributing the N spins!. The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.e g , site correlation parameter pg , maximal magnetization mg , and fraction of unfrustrated bonds hg . A set of 500 samples is considered for each size N ~number of spins! and array ~way of distributing the N spins!. The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.hg . A set of 500 samples is considered for each size N ~number of spins! and array ~way of distributing the N spins!. The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.N spins!. The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.