Size and Shape Dependence for Triangular and Honeycomb Finite Lattices with Mixed Exchange Interactions

Abstract

By means of exact numerical calculations, the properties of small lattices with mixed exchange interactions (or bonds) are studied. A particular bond can be either ferromagnetic (F) or antiferromagnetic (AF). We assume equal magnitudes and equal concentrations for each kind of bonds. An important independent variable is the number of spins (N) or size of the lattice. We consider here two different two-dimensional geometries: triangular lattices (TL) and honeycomb lattices (HL).1 The maximum size is 42 for TL and 64 for HL. The distribution of these spins considers all possible rectangular and square arrays. The shape is an interesting independent variable. Each distribution of bonds for a given array is a sample. Once the sample is generated no mutation or migration of bonds is allowed. Thus for each sample the distribution of bonds is fixed. Periodic boundary conditions are used to keep the coordination number constant through the lattice. To get a statistical representation of these systems, 500 samples are considered for each array. Our main interest is to study the properties of the ground level of these lattices and their dependence with size and shape. In the present article we report the following properties for TL and HL: average energy per bond, remnant entropy, and order parameters p and h.2 The results agree well with the expected behavior toward the thermodynamic limit. A comparison with similar results reported for square lattices (SL) will be also performed. A deeper discussion is carried out for the recently defined order parameters p and h.2,3 Open image in new window Figure 1 Distribution of sites for a triangular lattice (filled circles) and for a honeycomb lattice (open circles).