# Introduction

We have seen in Long range correlations that as a given system approaches a critical point, the distance ${\displaystyle \xi }$ over which the fluctuations of the order parameter are correlated becomes comparable to the size of the whole system and the microscopic aspects of the system become irrelevant (which is the phenomenon of universality we have encountered in Critical exponents and universality ). This means that near a critical point the system has no longer characteristic lengths, besides ${\displaystyle \xi }$ of course. We can therefore expect that if we "move" a little bit from a critical point, for example changing the temperature by a small amount, the free energy of the system as a function will not change its shape, but will be rescaled.

This is the main idea of scaling theory; in order to understand it the concept of homogeneous function is essential, and in appendix Homogeneous functions we recall the most important facts about them.