The critical isotherms at are given by

where δ is the critical isotherm exponent.

The divergence of correlation length ζ below and above can be described as

where and ν are the correlation length exponents below and above .

The correlation functions for the fluid and magnetic systems at the critical point go as

where d is the space dimension and η is an exponent.

It is now necessary to know how to extract the critical exponent describing the leading singularity of a thermodynamic quantity when it is in the form of a power series.

3. Extraction of critical exponents:

Let us take a general function F(t) as

and the function is singular at t =0 . We are now interested in extracting the exponent λ. Let us take the following limit

and one might see that after taking the limit, the exponent λ is given by

................................................... ...........................................................(3.1)

Note that F(t) is just not given by

For example, let us take a function and find the exponent λ describing the leading singularity of the function in the limit As per definition,