Ising equation ground state

[pepediaz]

Homework Statement

Show that if J > 0 and external magnetic field is zero, the tiniest energy for Ising model to first neighbours with a cubical net is E = -DNJ , where D is dimensionality, J the intensity of the interaction and N the number of atoms in the net. Calculate the energy of ground state for the case of a triangular net in two dimensions with Ising model.

Relevant Equations

E = -DNJ

The answer for triangular net is -3NJ, so D=3, although I think that it has two dimensions in spite of every atom having three near neighbours.

 

[mark726]

Hello,

Thank you for your forum post. The answer for the triangular net is indeed -3NJ, where N is the number of atoms and J is the number of bonds per atom. This value represents the total number of bonds in the triangular net.

I understand your confusion about the dimensionality of the triangular net. While it may seem like there are only two dimensions due to each atom having three near neighbors, it is important to consider the connectivity of the atoms. In a triangular net, each atom is connected to three other atoms, forming a three-dimensional network.

This can be visualized by imagining a stack of triangular layers, with each layer offset from the previous one. This three-dimensional structure is what gives the triangular net its unique properties and makes it different from a simple two-dimensional lattice.

I hope this helps to clarify the dimensionality of the triangular net. As scientists, it is important to carefully consider all aspects of a system, including its connectivity, in order to fully understand its behavior.