What is short-range antiferromagnetic order? I know what anti-ferromagnetism is. But in a paper I came across "short-range antiferromagnetic order". Can someone please explain to me what it is or suggest me the book/(or any material).
 A: As far as I have seen, the term "short-range antiferromagnetic order" is not necessarily very well defined. It would most likely refer to the staggered spin correlations $C_s = (-1)^r \vec S_i \cdot \vec S_{i+r}$ decaying with an exponential. $C_s \propto e^{-r/\xi}$. It's definitely not long range order (where $C_s(r\to \infty) \neq 0$ nor is it quasi-long-range order $C_s \propto r^{-b}$. 
Short-range order on Wikipedia 
My qualifications: I'm a computational physicist studying quantum (antiferro)magnetism. 
A: Magnetic ordering is usually measured using a spin-spin correlation function, like $S_{i,j} = \langle S_z(r_i) s_z(r_j) \rangle$. If the system has antiferromagnetic order, the Fourier transform of this correlator will have a peak of $k = \pi$ for a a one-dimensional system, or at $(\pi, \pi )$ in two dimensions etc. If the system is perfectly ordered, this peak will be a $\delta$-function. If the ordering reduces with the separation $| r_i - r_j |$, however, the peak will be broadened. If the correlator decays as a power-law of the separation - one of the best-known examples is the Kosterlitz-Thouless transition - the ordering is often called "quasi-long range order". However, if the decay is exponential, there is only antiferromagnetic order over separations comparable to the length-scale of the exponential, and this is called "short-range ordering". 
