What is spin on a lattice site is it electrons or atom as a whole? Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d? 
 A: The spin referred in condensed matter is the spin of the electrons least bound to the atoms (usually valance electrons). The atoms reside on the lattice sites. A spin half problem means the atoms have only one valance electron. But there are other possibilities like spin 1, 3/2 and all. As qeb has already mentioned it can also be used for nuclear spins also. I just want mention that any two level quantum system can be represented as a effective spin 1/2 problem.
A: A spin-half on a lattice site is a theoretical 'particle' with the property of having a spin of one half. It can be either 'up' or 'down' along the measuring-axis (in most textbooks the spin operator for assigning spin up-or down is the $\sigma_z$ operator, the third Pauli matrix. You could also use the $\sigma_x$ or $\sigma_y$.
I believe the spin on a site arises from an electron or nucleus residing at said lattice site.
In the context of lattice physics, you have electron-hopping problems, but also spin-hopping problems (for instance the Kitaev model in 2D: http://arxiv.org/abs/cond-mat/0506438).
These are different physical systems. In the electron hopping, the electrons hop from site to site, whereas for spin-hopping, the system that provides the spin [the electron or nucleus] changes properties, such that you can speak of an effective hopping of a spin 'particle'.
I hope this helps
A: Well I had an extensive discussion  with experimentalist friend and he tells me that its the unfilled electrons i.e d-orbitals...... yea it can be more than spin half but we are discussing hopping in a lattice then it is a single electron with spin half and in condensed matter(since we cannot have more than one electron to hop from the same site) it is the spin half which matters.....as far as nuclear is concern its even more complicated and can be best understood from lattice gauge theory. which was not my question......my question was on lattice in condensed matter............   
