Ising model, Hiblert space, Hamiltonian

[newbe318]

Can anyone please explain to me what is the Ising model, Hilbert space, and
Hamiltonian ?

However, please explain it as simple as possible because I am a freshman.

I have looked up all three things. I've tried my best to make some sense of it, but I am, honestly, still confused on what any of it means. I hate to ask silly questions, but What is the purpose of the Ising model, Hilbert space, and Hamiltonian? What are some important details that I should, at the very least, need to take away from learning these topics?

I am researching on an physical review paper and I need help understanding what those three topics mean. Any knowledge or help given on topic to help me better understand is appreciated. Thank you.

 

[VantagePoint72]

What is the purpose of the Ising model, Hilbert space, and Hamiltonian? What are some important details that I should, at the very least, need to take away from learning these topics?

Hilbert spaces and Hamiltonians are the foundation of quantum mechanics, so if you're confused by what they mean then it sounds like you have a pretty significant knowledge gap to understanding something like the Ising model. A Hilbert space is the set of all possible states of quantum system, which together form something you learn about in linear algebra called a vector space. The Hamiltonian determines how a quantum system changes with time. The Ising model is a particular Hamiltonian that is used as a model for understanding ferromagnetism quantum mechanically. Without learning the basics of quantum mechanics first, as one would do in a typical first or second year physics class, I don't really see that understanding a particular application of quantum mechanics like the Ising model is possible. In any case, it doesn't seem like usual freshman material.

 

[newbe318]

Thank you for helping me.

In case you're wondering, yes it doesn't seem like freshman material because my partners are the one who decided to research this topic for our presentation.