Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on:
- the dimension of the system
- the range of the interaction
- the spin dimension
These properties of critical exponents are supported by experimental data. Analytical results can be theoretically achieved in mean field theory in high dimensions or when exact solutions are known such as the two-dimensional Ising model. The theoretical treatment in generic dimensions requires the renormalization group approach or the conformal bootstrap techniques. Phase transitions and critical exponents appear in many physical systems such as water at the liquid-vapor transition, in magnetic systems, in superconductivity, in percolation and in turbulent fluids. The critical dimension above which mean field exponents are valid varies with the systems and can even be infinite. It is 4 for the liquid-vapor transition, 6 for percolation and probably infinite for turbulence.[1]Mean field critical exponents are also valid for random graphs, such as Erdős–Rényi graphs, which can be regarded as infinite dimensional systems.[2]
https://en.wikipedia.org/wiki/Critical_exponent
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