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My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical Mechanics by Sacha Friedli and Yvan Velenik (The Book Project can be seen here) that talked about magnetization $M_N$ (chapter 1 pages 17 and 20).

My question about the Ising model is the following.

What conceptually mean fluctuation of the magnetization $M_N$? And large fluctuations of $M_N$?

Up date: Surely this question is related to another concept: fluctuations of spins.

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Quantitative mean of fluctuation is the variance of magnetization $\sigma_M$ –  hwlau Apr 19 at 14:42
    
@hwlau Hello. Have some reference to this definition? –  Elias Apr 19 at 21:54
    
@Elias: if you have specific questions about our book, please do not hesitate to ask us directly (the relevant email address is given on the book page). For us, it is important to know what are the parts that should be clarified. –  Yvan Velenik Apr 25 at 12:38
    
@YvanVelenik, Thank you. If my doubt is useful I will be happy to send it by email. –  Elias Apr 25 at 20:39

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