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I acknowledge that this question is quite trivial. But in the lattice jargon, what does a $N$-sites lattice mean?

  • it's a lattice $N\times N$ or
  • it's a lattice with $N$ vertices?
  • another option perhaps.

From the context I cannot infer it. I just know that $N$ is quite large, i.e. in the thermodynamic limit $N\to \infty$, one also has $N^2\to\infty$ and $N^{1/2}\to\infty$.


Edit: The lattice is in 2D.

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"Site" is synonymous with "vertex". They're called "sites" because they're the places where the objects of interest (particles with a spin or whatever) are located. So it's a lattice with $N$ vertices.

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  • $\begingroup$ Ok, so, for a finite $d$-dim lattice with $N$ sites, if equally spacially distributed, you got a $N^{1/d}\times\ldots\times N^{1/d}$ array, right? $\endgroup$ – c.p. Oct 28 '13 at 15:20
  • $\begingroup$ Yes, exactly, though I guess in general it could be some shape other than a $d$-cube. $\endgroup$ – Nathaniel Oct 28 '13 at 15:58

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