Critical exponents are defined in terms of the variation of certain physical properties of the system near its phase transition point. These physical properties will include its reduced temperature ${\displaystyle \tau }$ , its order parameter measuring how much of the system is in the "ordered" phase, the specific heat, and so on.

• The exponent ${\displaystyle \alpha }$  is the exponent relating the specific heat C to the reduced temperature: we have ${\displaystyle C=\tau ^{-\alpha }}$ . The specific heat will usually be singular at the critical point, but the minus sign in the definition of ${\displaystyle \alpha }$  allows it to remain positive.
• The exponent ${\displaystyle \beta }$  relates the order parameter ${\displaystyle \Psi }$  to the temperature. Unlike most critical exponents it is assumed positive, since the order parameter will usually be zero at the critical point. So we have ${\displaystyle \Psi =|\tau |^{\beta }}$ .
• The exponent ${\displaystyle \gamma }$  relates the temperature with the system's response to an external driving force, or source field. We have ${\displaystyle d\Psi /dJ=\tau ^{-\gamma }}$ , with J the driving force.
• The exponent ${\displaystyle \delta }$  relates the order parameter to the source field at the critical temperature, where this relationship becomes nonlinear. We have ${\displaystyle J=\Psi ^{\delta }}$  (hence ${\displaystyle \Psi =J^{1/\delta }}$ ), with the same meanings as before.
• The exponent ${\displaystyle \nu }$  relates the size of correlations (i.e. patches of the ordered phase) to the temperature; away from the critical point these are characterized by a correlation length ${\displaystyle \xi }$ . We have ${\displaystyle \xi =\tau ^{-\nu }}$ .
• The exponent ${\displaystyle \eta }$  measures the size of correlations at the critical temperature. It is defined so that the correlation function scales as ${\displaystyle r^{-d+2-\eta }}$ .
• The exponent ${\displaystyle \sigma }$ , used in percolation theory, measures the size of the largest clusters (roughly, the largest ordered blocks) at 'temperatures' (connection probabilities) below the critical point. So ${\displaystyle s_{\max }\sim (p_{c}-p)^{-1/\sigma }}$ .
• The exponent ${\displaystyle \tau }$ , also from percolation theory, measures the number of size s clusters far from ${\displaystyle s_{\max }}$  (or the number of clusters at criticality): ${\displaystyle n_{s}\sim s^{-\tau }f(s/s_{\max })}$ , with the ${\displaystyle f}$  factor removed at critical probability.

For symmetries, the group listed gives the symmetry of the order parameter. The group ${\displaystyle \mathrm {Dih} _{n}}$  is the dihedral group, the symmetry group of the n-gon, ${\displaystyle S_{n}}$  is the n-element symmetric group, ${\displaystyle \mathrm {Oct} }$  is the octahedral group, and ${\displaystyle O(n)}$  is the orthogonal group in n dimensions. 1 is the trivial group.

• Universality classes from Sklogwiki
• Zinn-Justin, Jean (2002). Quantum field theory and critical phenomena, Oxford, Clarendon Press (2002), ISBN 0-19-850923-5
• Ódor, Géza (2004). "Universality classes in nonequilibrium lattice systems". Reviews of Modern Physics. 76 (3): 663–724. arXiv:cond-mat/0205644. Bibcode:2004RvMP...76..663O. doi:10.1103/RevModPhys.76.663. S2CID 96472311.
• Creswick, Richard J.; Kim, Seung-Yeon (1997). "Critical Exponents of the Four-State Potts Model". Journal of Physics A: Mathematical and General. 30 (24): 8785–8786. arXiv:cond-mat/9701018. doi:10.1088/0305-4470/30/24/036. S2CID 16687747.