Array of magnets around a sphere

[intervoxel]

An array of N magnets which can turn freely about their centers in any direction in 3d space is distributed uniformly around a spherical surface (their centers). What is the configuration of equilibrium of the system after some time? (minimum energy)

Do you know of any work showing that?

Thanks.

 

[j824h]

How much 'uniformly' do you mean? You know, N discrete magnets cannot be in a uniform distribution.

What are the exact locations of the magnets? To get quantitative result, we need more specific information than just that they are on a sphere. I think I can get some numerical solutions once I have an idea about the initial conditions.

 

[CWatters]

It's not possible to make a spherical magnet with one pole inside and the other outside. If you try you won't get the result you might hope for.

 

[Brinx]

This post refers to simulation software that can be used to study the Ising model on curved surfaces:

https://www.physicsforums.com/showthread.php?t=409671

This work treats 'sphere-like' lattices, such as a pillow-shaped one and a cube projected onto a sphere:

http://arxiv.org/pdf/hep-lat/9602025.pdf

Is this the kind of work you are looking for?

 

[intervoxel]

How much 'uniformly' do you mean? You know, N discrete magnets cannot be in a uniform distribution.

What are the exact locations of the magnets? To get quantitative result, we need more specific information than just that they are on a sphere. I think I can get some numerical solutions once I have an idea about the initial conditions.

Thanks for your reply, j824h. I was thinking of points belonging to a cubic lattice nearest to a spherical surface of integer radius.