Critical exponent

A critical exponent describes a power-law singularity near a continuous phase transition, such as $\xi \sim |t{|}^{-\nu }$ or $\chi \sim |t{|}^{-\gamma }$.

The reduced temperature is a dimensionless distance from a critical temperature. Multiplying it by a nonzero constant does not change any critical exponent.

The heat-capacity critical exponent is defined by the singular part $c_{\mathrm{s}}\sim |t{|}^{-\alpha }$ as the reduced temperature tends to zero.

The order-parameter critical exponent is defined in the ordered phase by $m\sim (-t{)}^{\beta }$ at zero conjugate field.

The magnetic-susceptibility critical exponent is defined by the zero-field magnetic susceptibility $\chi \sim |t{|}^{-\gamma }$. Separate amplitudes, and occasionally separate exponents, may occur on the two sides of the transition.

The critical-isotherm exponent is defined at the critical temperature by $m\sim |B{|}^{1/\delta }$ as the conjugate field $B$ tends to zero.

The correlation-length critical exponent is defined by $\xi \sim |t{|}^{-\nu }$. At a renormalization-group fixed point, its reciprocal is the positive eigenvalue of the temperature-like scaling direction.