Understanding Energy and Spin Interactions in the Ising Model

[iking]

Hello, actually, I am not a physicist, I am a Computer Science Graduate Student,
Anyways, I am doing a research related to Ising Model

My question is about the energy in Ising Model
the following statement is written in "History of the Lenz-Ising Model" paper:
"when two neighboring spins are the same (both +1 or -1) the energy is -U,
and when two neighboring spins are different, the energy is +U. In other words,
the interaction tends to make neighboring spins the same"

I know that my question is dumb, so please forgive me for that,:
what does a negative energy means?! and why a negative energy means
the interaction tends to make the neighboring spins the same?

Please forgive me for such questions.

Thanks

 

[SpectraCat]

Hello, actually, I am not a physicist, I am a Computer Science Graduate Student,
Anyways, I am doing a research related to Ising Model

My question is about the energy in Ising Model
the following statement is written in "History of the Lenz-Ising Model" paper:
"when two neighboring spins are the same (both +1 or -1) the energy is -U,
and when two neighboring spins are different, the energy is +U. In other words,
the interaction tends to make neighboring spins the same"

I know that my question is dumb, so please forgive me for that,:
what does a negative energy means?! and why a negative energy means
the interaction tends to make the neighboring spins the same?

Please forgive me for such questions.

Thanks

First of all, welcome to PF iking!

Second, your question is not at all dumb. Generally speaking, when you are considering the *relative* energies of two systems in physics, you are free to set the reference energy anywhere that is convenient, as long as you are consistent. In the context of this example, the aligned spins have a stabilizing interaction, which lowers the overall energy of the system by the amount U ("more stable" means "lower energy" in physics parlance). The anti-aligned spins have a destabilizing interaction, which raises the overall energy of the system by the amount U. So, if we choose the reference energy to be the system of non-interacting spins, then we have the sign convention from your post, where aligned spins contribute -U and anti-aligned spins contribute +U.

HTH!

 

[iking]

Thank you so much SpectraCat, your explanation was really helpful.

I have another question:
why do we conclude that this interaction tends to make neighboring spins the same?
I mean you said "aligned spins have stabilizing interaction", do u mean that physical
systems tends towards lower-energy state?

Thank you again for your patience.

 

[SpectraCat]

Thank you so much SpectraCat, your explanation was really helpful.

I have another question:
why do we conclude that this interaction tends to make neighboring spins the same?
I mean you said "aligned spins have stabilizing interaction", do u mean that physical
systems tends towards lower-energy state?

Yes, that is a general principle of physics. So, in the absence of thermal fluctuations that can add energy and "randomize" the spins, the system will always tend towards the maximally-aligned state representing the lowest energy.

 

[iking]

THANK YOU SO MUCH, That was really really helpful
Thank you again.
:)