Critical exponents

Reduced distance: $\epsilon$

$\epsilon$ is the reduced distance from the critical temperature, i.e.

$\epsilon =\left|1-{\frac {T}{T_{c}}}\right|$

Note that this implies a certain symmetry when the critical point is approached from either 'above' or 'below', which is not necessarily the case.

Heat capacity exponent: $\alpha$

The isochoric heat capacity is given by $C_{v}$

$\left.C_{v}\right.=C_{0}\epsilon ^{-\alpha }$

Experimentally $\alpha =0.1105_{-0.027}^{+0.025}$.

Magnetic order parameter exponent: $\beta$

The magnetic order parameter, $m$ is given by

$\left.m\right.=m_{0}\epsilon ^{\beta }$

Susceptibility exponent: $\gamma$

Susceptibility

$\left.\chi \right.=\chi _{0}\epsilon ^{-\gamma }$

Correlation length

$\left.\xi \right.=\xi _{0}\epsilon ^{-\nu }$

Rushbrooke equality

The Rushbrooke equality , proposed by Essam and Fisher (Eq. 38 ) is given by

$\alpha +2\beta +\gamma =2$

Gamma divergence

When approaching the critical point along the critical isochore ($T>T_{c}$) the divergence is of the form

$\left.\right.C_{p}\sim \kappa _{T}\sim (T-T_{c})^{-\gamma }\sim (p-p_{c})^{-\gamma }$

where $\gamma$ is 1.0 for the Van der Waals equation of state, and is usually 1.2 to 1.3.

Epsilon divergence

When approaching the critical point along the critical isotherm the divergence is of the form

$\left.\right.\kappa _{T}\sim (p-p_{c})^{-\epsilon }$

where $\epsilon$ is 2/3 for the Van der Waals equation of state, and is usually 0.75 to 0.8.

See also

• Universality classes