# What is a bulk phase transition?

I have been able to google "bulk phase transition" and get plenty of results that verify that something called a bulk phase transition exists, however, I cannot seem to find a precise definition of what exactly a bulk phase transition is. Could someone please help me with a definition of bulk phase transition? I would very much appreciate it.

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I'm not an expert so I won't submit it as a definitive answer but when it comes to complex physical terms I find it helpful to break them down into their constituent parts. A phase transition occurs when a material changes phase (liquid -> gas, gas -> solid, etc.). When talking about materials the term "Bulk" generally refers to a volume. So putting the terms together, it would seem that a "bulk phase transition" would be when an entire material changes phase at once. – Michael Leonard Oct 22 '12 at 20:28
@MichaelLeonard Thanks for the input. I was under the impression when we said "phase transition" we always meant the entire system under consideration was undergoing a change. Do you think "bulk" is simply extra? or is my understanding of normal phase transitions off? – kηives Oct 23 '12 at 22:18
I have the same confusion as you on that. I did stumble across one paper that mentioned a comparison of Surface Phase transition vs. Bulk Phase transition. That would seem to indicate that there is at least some meaningful difference. If I were to take a guess, I would think bulk phase transition would be when the entire material undergoes a phase transition (i.e. sublimation) vs surface phase transition where just the surface of the material is undergoing a phase transition (i.e. water freezing on a lake) – Michael Leonard Oct 24 '12 at 3:06
@kηives: Yes, this is by opposition to, e.g., surface phase transitions. A typical example of the latter is the wetting transition. – Yvan Velenik Oct 24 '12 at 7:05
@MichaelLeonard If you would like to write up an answer I'll approve FYI, since that seems to be the consensus, however small. – kηives Oct 24 '12 at 14:25

I think the word bulk transition is used in several (related) contexts. The first is the following: Consider a system with a first order phase transition, governed by some partition function in $d$ dimensions. Impose boundary conditions that create a $d-1$ dimensional interface between the two phases. Construct an effective partition function (in $d-1$ dimensions) for the interface. You can now ask whether the roughening transition for the $d-1$ dimensional interface occurs at the same temperature as the $d$ dimensional bulk transition.

A (related) usage of the term bulk transition is in lattice field theory, usually in the context of first order transitions of lattice gauge theories at strong coupling. A weak coupling transition of a $d+1$ dimensional lattice model is related to a thermal phase transition of a continuum field theory in $d$ spatial dimensions. But this is not the case for a strong coupling transition -- there is no continuum limit, and therefore no thermal interpretation of the boundary conditions. The transition is merely a bulk transitions of the $d+1$ dimensional lattice model.

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"Impose boundary conditions that create a d−1 dimensional interface between the two phases." You mean if I'm in three-dimensions, construct a two-dimensional sheet of critical points? I don't understand how the b.c. relate to constructing a a $d-1$ dimensional critical surface. – kηives Nov 28 '15 at 17:25
Take a 3d Ising model. Fix all spins at z=0 to be up, and all spins at z=L down. At sufficiently low T this will create a 2d interface. You can now try to construct an effective partition fct for the 2d surface, and ask whether the 2d (roughening) transition takes place at the same T as the 3d Ising (bulk) transition. See, for example, arxiv.org/abs/hep-lat/9601011 – Thomas Nov 28 '15 at 19:57
"for the 2d surface", what 2d surface? How are you using the word "interface" in this context? – kηives Nov 29 '15 at 16:08
In the usual sense: Take a 3d system. Force spins up at the bottom, down at the top. Then there will be a domain of up spins, and one of down spins that meet at an interface somewhere in the middle. This interface is a dynamical object, described by its own 2d theory. – Thomas Nov 29 '15 at 23:50
Thanks, I only know the term "domain wall," so I needed that extra explanation. – kηives Nov 30 '15 at 3:40

I think you should not put the question in such a way: "What exactly a bulk phase transition is?" concerning such matters. It is because it is not a precisely defined scientific term. It is rather an explanatory term that people may use to indicate different things. In such a case they, of course, should explain, what do they mean.
I am one of those who often uses the term "bulk phase transition". I use it to stress the difference between the transition taking place in the whole (or most of) the material bulk and the one only taking place locally. The local case may take place say, when the transition into the daughter phase takes place say, in the vicinity of a surface or of some defect, like say, a dislocation or an inclusion, while the bulk of the body stays in the mother phase. I hope it helps.

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I would say that a bulk phase transition can appear in a liquid or a solid. In a liquid however the differences would be less pronounced since the difference between the bulk and the surface is only some interface energies. In solid state phase transitions (normally reffered to as transformations) the strain energy also depicts a major contribution to the Gibbs free energy (analogy of pressure in gases). Therefore, since these stresses are lower near unconstrained surfaces, one could use the term bulk phase transition to restrict his representative volume element fully to a bulk, e.g. by applying periodic boundary conditions

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