Multicritical point

At least two thermodynamic or other parameters must be adjusted to reach a multicritical point.

A more detailed definition requires concepts from the theory of critical phenomena.

The parameter space here is the temperature axis, and the critical manifold consists of the point

Under hydrostatic pressure the substance normally still becomes ferromagnetic below a temperature

as a thermodynamic parameter leads to a critical surface

However, criticality terminates for good reason, and the points on the borders normally belong to another universality class than the universality class realized within the critical manifold.

Instead of terminating somewhere critical manifolds also may branch or intersect.

At least two parameters must be adjusted to reach a multicritical point.

The gas-liquid critical point is not multicritical, because the phase transition at the vapour pressure curve

) is discontinuous and the critical manifold thus consists of a single point.

To reach a tricritical point the parameters must be tuned in such a way that the renormalized counterpart of the

A well-known experimental realization is found in the mixture of Helium-3 and Helium-4.

To reach a Lifshitz point the parameters must be tuned in such a way that the renormalized counterpart of the

A Lifshitz point is realized in a prototypical way in the ANNNI model.

Hornreich, S. Shtrikman and M. Luban in 1975, honoring the research of Evgeny Lifshitz.

This multicritical point is simultaneously tricritical and Lifshitz.

Three parameters must be adjusted to reach a Lifshitz tricritical point.

Such a point has been discussed to occur in non-stoichiometric ferroelectrics.

The critical manifold of an Ising model with zero external magnetic field consists of the point at the critical temperature

In a purely imaginary external magnetic field

this critical manifold ramifies into the two branches of the Lee-Yang type, belonging to a different universality class.

[1] The Ising critical point plays the role of a multicritical point in this situation (there are no imaginary magnetic fields, but there are equivalent physical situations).

A critical curve terminating at a multicritical point (schematic).
The critical point of the Ising model with critical temperature ramifies into the two branches of the Lee-Yang critical manifold in an imaginary magnetic field for (schematic).