# What does “sites” mean in the lattice language?

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.

"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.
• 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? – c.p. Oct 28 '13 at 15:20
• Yes, exactly, though I guess in general it could be some shape other than a $d$-cube. – Nathaniel Oct 28 '13 at 15:58