Isn't "fluctuations of the order parameter" a wrong terminology in here?

Question

In the book Statistical Field Theory by Giuseppe Mussardo, on page 11, it is given that

Aspects of phase transitions. It is now useful to stop and highlight the aspects of phase transitions that have emerged so far. The most important property is that at $T=T_{c}$, the fluctuations of the order parameter extend significantly to the entire system, while they are exponentially small away from the critical point.

However, what do they mean by "fluctuations of the order parameter"?
To my understanding, what extends to the entire system is the correlation length, not the fluctuations in the order parameter. I mean, when one says "fluctuations", to me, it refers to something related to the variance of the random variable in question. But that is not the case, so I'm confused

GiorgioP · Accepted Answer

The correlation length is defined in terms of the distance dependence of the correlation of the order parameter fluctuations at different points.
$$
G(r) = langle delta m(r+r') ~delta m(r') ranglepropto frac{e^{-r/xi}}{r}.
$$
Divergence of the correlation length $xi$ implies long-range correlations requiring long-range fluctuation of the order parameter.

Isn't "fluctuations of the order parameter" a wrong terminology in here?

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