Question

Why is the upper critical dimension of the Ising model 4?

Answer 1

I have read in various sources, that the critical exponents of the Ising Model are identical to the meanfield ones for dimensions d≥4d≥4. In trying to understand this better I came across the Ginzburg Criterion and the concept of upper critical dimension. I'm new to this field and unfortunately not able to see dcrit=4dcrit=4 starting from the definition of the Ising Model. Do you have a literature suggestion, where this is derived in a beginner-friendly fashion? Or can you give me a hint on how the Wikipedia page on the upper critical dimension could be related to the Ising Model.

hope this helps......

Answer 2

The critical exponents of the Ising Model are identical to the meanfield ones for dimensions d≥4d≥4. In trying to understand this better I came across the Ginzburg Criterion and the concept of upper critical dimension. I'm new to this field and unfortunately not able to see dcrit=4dcrit=4 starting from the definition of the Ising Model.