Widom scaling

Widom scaling (after Benjamin Widom) is a hypothesis in statistical mechanics regarding the free energy of a magnetic system near its critical point which leads to the critical exponents becoming no longer independent so that they can be parameterized in terms of two values. The hypothesis can be seen to arise as a natural consequence of the block-spin renormalization procedure, when the block size is chosen to be of the same size as the correlation length.

Widom scaling is an example of universality.

The critical exponents ${\displaystyle \alpha ,\alpha ',\beta ,\gamma ,\gamma '}$ and ${\displaystyle \delta }$ are defined in terms of the behaviour of the order parameters and response functions near the critical point as follows

where

Near the critical point, Widom's scaling relation reads

where ${\displaystyle f}$ has an expansion

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