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I'd like to check the correctness of a simulation I ran on the Ising model on a triangular by verifying if I get the good value of the mean energy per site. I found a formula giving it for high temperatures on a square lattice but nothing on the triangular case. My simulation focuses on the critical point so I guess that both the high energy and low energy expansion should work.

Do you have a reference or a link to this expression? Are there more accurate/relevant test to check that my system is really at criticality (except looking at the correlations functions which I already checked unsuccessfully...)

Thank you in advance!

Learning is a mess
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    Check the characteristic heat, it should diverge. – jgyou Nov 06 '13 at 13:28
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    As well as http://nuweb9.neu.edu/fwu/wp-content/uploads/Wu100_JSP40_613.pdf. He obtains the free energy per site. It is pretty straightforward from there. – jgyou Nov 06 '13 at 13:32
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    Last comment I swear! I forgot to add that the isothermal susceptibility diverges too. You can obtain both this quantity and the specific heat using the easily provable formulas: $\chi_T = \beta(\langle M^2 \rangle -\langle M\rangle^2)$, with $M$ the magnetization, and $C_M = (\langle E^2 \rangle -\langle E\rangle^2)/(k_b T^2)$ – jgyou Nov 06 '13 at 13:36
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    Thank you very much JGab for the suggestions, I'm already looking into that, I'll let you know of my progress ;) – Learning is a mess Nov 06 '13 at 13:57
  • Someway yes, plotting the magnetization helped me in finding more precisely the critical point that the susceptibility which were really noisy plots. At least it decided me in looking at cluster flipping algorithms around criticality. Thank you again. – Learning is a mess Nov 11 '13 at 19:30
  • Long shot, but @jgyou do you happen to have the author's name for that paper / have a copy? That university has changed their domain and the link is broken. – Zxv May 27 '22 at 07:30

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