Interesting phenomena can be expected in systems that admit more complicated phase diagrams. The massive complex scalar field for example, admits stable stars as well as black holes and flat space as possible end states. There are three phase boundaries, and these should intersect somewhere. A generic two-parameter family of initial data is expected to intersect each boundary in a line, and the three lines should meet at a triple point.

Similarly, many systems admit both type I and type II phase
transitions, for example the massive real scalar field, and the
*SU*
(2) Yang-Mills field in spherical symmetry. In a two-dimensional
family of initial data, these should again generically show up as
lines, and generically these lines should intersect. Is the black
hole mass at the intersection finite or zero? Is there a third
line that begins where the type I and type II lines meet?

Choptuik, Hirschmann and Marsa [42] have investigated this for a specific two-parameter family of
initial data for the spherical
*SU*
(2) Yang-Mills field, using a numerical evolution code that can
follow the time evolutions for long after a black hole has
formed. As known previously, the type I phase transition is
mediated by the static Bartnik-McKinnon solution, which has one
growing perturbation mode. The type II transition is mediated by
a DSS solution with one growing mode. There is a third type of
phase transition along a third line which meets the intersection
of the type I and type II lines. On both sides of this ``type
III'' phase transition the final state is a Schwarzschild black
hole with zero Yang-Mills field strength, but the final state is
distinguished by the value of the Yang-Mills gauge potential at
infinity. (The system has two distinct vacuum states.) The
critical solution is an unstable black hole with Yang-Mills hair,
which collapses to a hairless Schwarzschild black hole with
either vacuum state of the Yang-Mills field, depending on the
sign of its one growing perturbation mode. The critical solution
is not unique, but is a member of a 1-parameter family of hairy
black holes parameterized by their mass. At the triple point the
family ends in a zero mass black hole.

Critical Phenomena in Gravitational Collapse
Carsten Gundlach
http://www.livingreviews.org/lrr-1999-4
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