Correlated Magnets: Interaction is N-ary

Correlated magnet interaction is N-ary, where N can be any desired number up to physical limitations of the magnetized material and technical limitations of the magnetization process. A given surface of a correlated magnet can have some number of magnetic sources, or maxels, depending on the size of each maxel and the size of the surface, where the maxels can have different shapes and sizes. Each maxel can have either positive or negative polarity. The maxels can also be magnetized to have different magnetic field strengths. Very importantly, the spatial force (i.e., attractive, repulsive, or no force) produced by two correlated magnetic structures depends on their relative spatial alignment and separation distance. So, N can be a very large number. 

The following discussion compares the interaction of two complementary magnetic structures that are not naturally stacked but instead are held in alignment in accordance with a Barker 3 code (++-) as depicted in Fig. 1.   

Fig. 1 Bar Magnets Stacked in Accordance with a Barker 3 Code

Two identical structures can be described as being complementary when spatially aligned such that their opposing faces mirror each other as shown in Fig. 2.  In other words, each magnetic source of each of the opposing face is opposite a source having the opposite polarity. 

Fig. 2 Complementary Correlated Magnetic Structures

The five Relative Alignments of the two complementary correlated structures are shown in Fig. 3. 

The possible alignments of the two complementary correlated magnetic structures correspond to a spatial correlation function depicted in Fig. 4, where aligning magnets can cancel each other out.

Fig. 4 Spatial Force Function of Complementary Correlated Magnetic Structures A and B

Two identical structures can be described as being anti-complementary when spatially aligned such that their equal faces mirror each other as shown in Fig. 2. In other words, each magnetic source of each of the opposing face is opposite a source having the same polarity. 

Fig. 5 Anti-Complementary Correlated Magnetic Structures

The possible alignments of the two anti-complementary correlated magnetic field structures correspond to a spatial correlation function depicted in Fig. 6, which is opposite the one shown in Fig. 4.

Fig. 6 Spatial Force Function of Anti-complementary Correlated Magnetic Field Structures A and B