Critical exponents

Specific heat, C

$C=C_0{ϵ}^{-\alpha }$

Magnetic order parameter, m,

$m=m_0{ϵ}^{\beta }$

Susceptibility

$\chi ={\chi }_0{ϵ}^{-\gamma }$

Correlation length

$\xi ={\xi }_0{ϵ}^{-\nu }$

where $ϵ$ is the reduced distance from the critical temperature, i.e.

$ϵ=|1-\frac{T}{T_c}|$

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

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

Gamma divergence

When approaching the critical point along the critical isochore ($T>T_c$) the divergence is of the form

$C_p\sim {\kappa }_T\sim (T-T_c{)}^{-\gamma }\sim (p-p_c{)}^{-\gamma }$

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

${\kappa }_T\sim (p-p_c{)}^{-ϵ}$

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

See also

• Universality classes