- #1
thatboi
- 130
- 20
Hi all,
I'm trying to see if my question/logic makes sense. Suppose I have a classical Ising model on a 2-D Square lattice with ##N## sites and 0 external field. There is an exact formula for the average internal energy per site, and at criticality it turns out to be ##u = -\sqrt{2}## where I have set the coupling constant ##J=1##. From here, I'd like to know if it is possible to find the average number of domain walls per site. I know each domain wall contributes energy ##2##. Now suppose the system is in its ground state (say all spin-up). Then the ground state energy is ##-2N##. I want to put in domain walls until the system energy increases to ##-\sqrt{2}N##, so we just need to solve ##-2N + 2n_{\text{walls}} = -\sqrt{2}N## and I get ##\frac{n_{\text{walls}}}{N} = \frac{2-\sqrt{2}}{2}##. Does this make sense?
I'm trying to see if my question/logic makes sense. Suppose I have a classical Ising model on a 2-D Square lattice with ##N## sites and 0 external field. There is an exact formula for the average internal energy per site, and at criticality it turns out to be ##u = -\sqrt{2}## where I have set the coupling constant ##J=1##. From here, I'd like to know if it is possible to find the average number of domain walls per site. I know each domain wall contributes energy ##2##. Now suppose the system is in its ground state (say all spin-up). Then the ground state energy is ##-2N##. I want to put in domain walls until the system energy increases to ##-\sqrt{2}N##, so we just need to solve ##-2N + 2n_{\text{walls}} = -\sqrt{2}N## and I get ##\frac{n_{\text{walls}}}{N} = \frac{2-\sqrt{2}}{2}##. Does this make sense?