Difference between corelation function and corelation lenght

For example if we look Ising model correlation function is
$$\langle S_iS_{i+j}\rangle$$
So we can see that if we took into acount just nearest neighbours interraction we also will see that some $$i+j$$-th spin feels i-th spin. So there is some correlation between them.
Am I right? This is correlation function. And what is correlation lenght?

Is it lenght between
$\uparrow\uparrow\uparrow\uparrow\downarrow\downarrow$
the biggest number of align spins?
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 If I watch some spin system, for example Ising model or something, what is for me there correlation lenght? Can you explain this to me?
 Recognitions: Science Advisor I'm not sure if the usage in condensed matter is the same, but usually the correlation function is more general. When the correlation function is exponential, exp(-x/L), then L is the correlation length. If the correlation function is a power law, x^n, then the correlation length is not defined (or "infinite", eg. http://www-thphys.physics.ox.ac.uk/p...18_Harvard.pdf says "power-law phase with infinite correlation length").

Difference between corelation function and corelation lenght

Yes, I think it's the same. Just in condensed matter I have maybe

$$\Gamma=exp(-\frac{an}{L})$$

where $$a$$ is distance between nearest neighbours. I don't understand very well that if I see phase transition in some point then correlation lenght there is pretty large. So $$\Gamma$$ goes to zero. Right?

And where I can have polynomial dependence? In ordered phase. Can someone explain me that?

Recognitions:
 Quote by LagrangeEuler Yes, I think it's the same. Just in condensed matter I have maybe $$\Gamma=exp(-\frac{an}{L})$$ where $$a$$ is distance between nearest neighbours. I don't understand very well that if I see phase transition in some point then correlation lenght there is pretty large. So $$\Gamma$$ goes to zero. Right? And where I can have polynomial dependence? In ordered phase. Can someone explain me that?