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.
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$\begingroup$ Can you link to the paper so we can see the context? $\endgroup$– taciteloquenceCommented Apr 12, 2020 at 7:28
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2 Answers
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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.
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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".
answered Apr 12, 2020 at 8:38
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$\begingroup$ So if we have a one dimensional spin chain of consecutive spin-up (say it is represented by 1 ) and spin-down (say it is represented by 0 ) and if the system is perfectly ordered then the spin chain will look like 1010101010101010101010 and this pattern will continue up to infinity. right...? And if the system has short-order ordering , then we will have 010101010 only upto a certain finite distance. $\endgroup$– physuCommented Apr 12, 2020 at 18:41
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$\begingroup$ Thanks for pointing out the typo in my answer. Yes, ...10101010... is an example of a perfectly ordered AF state. For a book, what type of system do you have in mind? $\endgroup$ Commented Apr 12, 2020 at 18:46
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$\begingroup$ About the book... I just wanted to study what you mentioned in your answer in detail. $\endgroup$– physuCommented Apr 12, 2020 at 18:50
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$\begingroup$ Almost any condensed matter textbook will discuss correlation functions. You can take a look at en.wikipedia.org/wiki/… to see the difference between ferromagnetic and antiferromagnetic correlation functions, and then look at the page's "Further reding". $\endgroup$ Commented Apr 12, 2020 at 18:57