The "Monte Carlo" term is deceivingly fancy, most algorithms with that label simply involve randomly picking from a set of possibilities (search space), as opposed to trying all cases or exploring in some other systematic way.

When you try do that for real problems, it can sometimes be difficult to sample from complex probability distributions/models efficiently in a way that is representative. There are lots of tricks around that, like most topics it's a black-hole of details. But it still boils down to randomly testing options.

Look at the source code, even in C it's really short and simple: https://github.com/msuzen/isingLenzMC/blob/master/src/isingL...

Statisticians like to do this kind of intellectual inflation, there are many such scary terms with simple meanings: "Markov Chain" is a process who's next state depends only on the current state, "stochastic" is a straight-up synonym for "random"... Illegitimi non carborundum!

I think there is a "correct" answer to this question! The best book on Monte Carlo methods is this one: https://artowen.su.domains/mc/

It's not published yet, but already a classic. (Might be more intermediate than beginner, though.)

For something a bit more gentle, I also recommend chapter 29 of this book: https://www.inference.org.uk/mackay/itila/book.html

I recommend starting here: https://youtu.be/nKCT-Cdk0xY

Once you understand and use this approach, you can figure out most other approaches you need to use.

this might be elementary but is a good introduction

https://archive.org/details/TheMonte-carloMethodlittleMathem...