Phase Transitions
When Everything Changes at Once
One Temperature for the Whole Piece
At ordinary pressure, ice melts at 0°C, and only there. A degree below, its molecules hold one another in a crystal; a degree above, the same molecules flow. Nothing about a molecule changes. What changes is how they are arranged, and they change it all together. Stir a glass of ice water as it warms, and the thermometer sits at 0°C until the last ice is gone: the heat goes into taking the crystal apart, not into speeding the molecules up. Melting a gram of ice takes as much heat as warming that gram of water by 80 degrees. Heat that flows in like this, with no rise in temperature, is called latent heat.
Why one exact temperature? Two pulls compete. The bonds between neighbors favor the tidy crystal, where each molecule sits in its best place. The count of arrangements favors the liquid: its molecules can be arranged in vastly more ways than a crystal’s, and the hotter it is, the more that count weighs. At one temperature the two pulls balance. Since each molecule’s place depends on its neighbors’, they tip together: below that temperature every bit of the crystal is stable, and above it none is. So the whole piece melts at that one temperature, as fast as heat reaches it.
A sharp melting point belongs to large numbers. A cluster of 139 sodium atoms melts at about −6°C, more than a hundred degrees below a lump of sodium, and gradually, over a range of temperatures. Grains of gold a few billionths of a meter across melt hundreds of degrees below gold’s melting point.
Waiting for a Seed
Water below 0°C should freeze, but freezing needs a start. A crystal must begin as a tiny cluster, and a tiny cluster is mostly surface, which costs more than its inside gains. Until a big enough cluster happens to form, or something offers a surface to grow on, such as a speck of dust or a scratch, the liquid stays liquid below its freezing point. It is supercooled. Cloud droplets, small and clean, stay liquid down to about −38°C, and droplets a few thousandths of a millimeter across, cooling by evaporation in a vacuum, have been caught still liquid below −42°C.
A reusable hand warmer is built on this. Its crystal melts at 58°C, yet the liquid sits at room temperature for months. Click the small metal disc inside, and a crystal starts at its rim and runs through the whole pack in seconds. The pack turns hot, up to about 54°C: the energy the liquid took in when it was melted comes back out as heat when it freezes. How the click starts the crystal is not fully settled; the leading explanation is specks of crystal that survive in the disc’s tiny cracks and are let loose when it bends.
Boiling can wait too. Water heated in a smooth cup in a microwave can pass 100°C and then boil over at the touch of a spoon, because a bubble of steam needs a start just as a crystal does. Melting almost never waits. A crystal heated past its melting point melts at once, because its surface starts to melt a little below that point and gives the liquid its seed. A crystal stays solid past its melting point only when its surface cannot start the melt: under a coating, or when it is heated from inside faster than melting can spread. Laser flashes have kept ice solid at almost 30°C for a billionth of a second.
A Jump or a Fade
What a phase transition changes is order. A liquid looks the same at every point and in every direction; a crystal repeats only at certain steps and angles. Freezing gives up that sameness, so a crystal is a broken symmetry. Physicists measure order with a quantity that is zero on the untidy side and grows on the tidy side, called the order parameter. For a magnet it is an arrow: how strongly, and which way, its tiny magnets agree.
A magnet shows this plainly. Iron’s atoms are tiny magnets, and each tends to line up with its neighbors. The push to line up is not their magnetic pull, which is far too weak; it comes from how their electrons repel one another and cannot share a state. Heat iron and more and more of them are knocked out of line, so its magnetism fades, and at 770°C, its Curie point, its own magnetism is gone; a magnet still pulls on it, but only weakly. There is no jump and no latent heat: the order shrinks smoothly to nothing, and is gone at one exact temperature. Freezing water jumps; the magnet fades. The two kinds are called first-order and continuous transitions.
Cool the iron again and the lining up returns, but nothing in the laws of physics prefers one direction to another. Patches form pointing different ways, grow, and merge, and in each patch one way wins by chance. The laws are symmetric; the magnet that obeys them is not. This is spontaneous symmetry breaking. The scene shows it in the simplest model, a flat sheet of tiny magnets that can point only two ways, where the patches merge until one way wins. A real piece of iron stops short of that. One patch would send a strong field out around it, which costs energy, so the iron settles into many patches pointing different ways, and their pulls cancel. That is why an iron nail is not a magnet until a magnet lines its patches up.
Where the Line Ends
Raise the pressure and water boils hotter: on the summit of Everest it boils near 70°C, in a pressure cooker near 120°C. Draw the boiling temperature against the pressure and you get a line, and the line stops at both ends. At its bottom, near 0°C and less than a hundredth of an atmosphere, ice, water and steam meet, and at lower pressures ice turns straight to vapor with no liquid at all. At its top, the line simply ends. At 374°C and 218 atmospheres, liquid water and its steam become alike: the same density, no surface between them, no heat needed to turn one into the other. That end is the critical point. Beyond it, water is one fluid, neither liquid nor gas.
Carbon dioxide gets there at a gentler 31°C and 73 atmospheres. Its line’s bottom end lies at 5 atmospheres, above ordinary air pressure, which is why dry ice on a table turns straight to gas and why liquid carbon dioxide must be sealed in. Sealed in a strong cell and heated, its liquid thins and its gas thickens, and the surface between them grows faint. Near the critical point the cell turns milky: patches of denser and thinner fluid of every size form and dissolve, and the largest grow as large as a wave of light, so they scatter it. This milky look is called critical opalescence. Past the point the cell is clear again, full of one fluid. In that state, carbon dioxide is used to take the caffeine out of coffee.
Because the line ends, there is a way round it. Squeeze liquid water past 218 atmospheres, heat it past 374°C, then let it expand while it is still that hot. It becomes steam without ever boiling. The melting line has no end that anyone has found. Liquid and gas have the same symmetry and differ only in how dense they are, so one can turn into the other bit by bit. A crystal either repeats or it does not, so there is no way from crystal to liquid without crossing the line.
Water may hide a second critical point, between two liquid waters, one denser than the other, deep in the cold where ice forms too fast to look. Glassy ice is ice with no crystal, its molecules stuck in a liquid’s jumble. A 2026 experiment melted it with brief laser flashes and caught the liquid with X-ray flashes before it could freeze. It found signs of a critical point near −63°C and 1,000 atmospheres: the liquid took more heat to warm by each degree, and its density flickered more. Some computer models put the point close by. Another group argues, from computer models of its own, that the signs come from the glass loosening as it melts. Until the patches of every size are measured there and the result is repeated, it is not settled.
Every Size at Once
Those patches of every size are the heart of a critical point. A magnet at its Curie point has them too: patches pointing one way inside patches pointing the other, with no favorite size, so that stepping back from the pattern leaves it looking the same. The details of the atoms are soon too small to matter. What survives at every scale is how many directions space has, how many ways the order can point, and whether the forces reach only to near neighbors.
So very different things share the same numbers. As a fluid nears its critical point, the difference between its liquid’s density and its gas’s shrinks as the distance to the critical temperature raised to a power of about a third, for neon, argon, xenon, nitrogen and carbon dioxide alike. A crystal whose tiny magnets can point only two ways along one axis, alternating up and down, loses that order by the same power, measured at 0.325. This is universality. Iron, whose tiny magnets can turn any way, belongs to a different family. Theory gives its family a power of about 0.37, and measurements on iron scatter around it. The method that explains it, called the renormalization group, works the way the scene does: it steps back and asks what survives.
Order can also be switched without warming or cooling. Physicists held 51 atoms in a row with laser tweezers, near absolute zero, and tuned a laser to sweep them from disorder into an ordered pattern, sometimes quickly, sometimes slowly. Near a critical point, distant parts of a system take longer and longer to agree, so a quick sweep leaves short ordered stretches. The stretches grew as the square root of how long the sweep took, the number theory gives for a row of two-way switches unsettled by quantum uncertainty instead of the jiggle of warmth. Left to settle, such a row belongs to the same family as the flat sheet in the scene, not the fluids’.
Order from Waves
Cold enough, order can come from quantum waves instead of bonds. Every atom travels as a wave, and the colder it is, the longer its wave. Cool a gas of rubidium atoms, ten million times thinner than air, to 170 billionths of a degree above absolute zero, and the waves grow longer than the gaps between the atoms. Thousands of atoms then fall into the one lowest state and move as a single wave. This is a Bose-Einstein condensate. Labs now make them routinely, and one has been made aboard the International Space Station, where it drifts freely for more than a second.
Common helium, helium-4, does something similar on its own below 2.17 degrees above absolute zero. Its atoms crowd too closely for all of them to share the lowest state, but under a tenth do, and that is enough to make the liquid a superfluid: part of it, and nearly all of it in the deeper cold, flows without friction through gaps too small for any ordinary liquid. Electrons cannot share one state, but in some materials, cooled enough, they team up in pairs, each pair spread wide enough to overlap many others. Together the pairs can share one state, and they then carry current with no resistance at all: superconductivity. Each is a phase transition, with its own temperature where its order sets in: one quantum wave keeping one rhythm across the whole piece.
As Universe Cooled
Universe itself went through such changes. About ten trillionths of a second after the Big Bang, near two million billion degrees, the Higgs field settled into the value it holds today. That value gives particles such as the W, the Z and the top quark their masses, and is expected to give the electron its own. Some ten to twenty millionths of a second after the Big Bang, near two trillion degrees, quarks and gluons, until then free in a hot liquid, were bound into protons and neutrons.
Neither was even a transition with one exact temperature, like the magnet’s. Computer calculations of both theories on a grid of points find a crossover: a smooth change spread over a range of temperatures, with no exact point, no patches of every size and no latent heat, like water going round the end of its boiling line. The scene shows the simple picture, with a moment when the hump first rises; in the full calculation there is no such moment. That matters for a question still open: why universe holds far more matter than antimatter. One proposal needs the Higgs change to have been a sharp jump, with bubbles of the new value growing like ice in supercooled water. The Standard Model gives a smooth change, so that proposal needs new particles that would make it sharp. A jump like that would have left a hum of gravitational waves, which a space observatory planned for launch around 2035, the Laser Interferometer Space Antenna, could hear. Another proposal needs no jump at all. None is confirmed.
The change from free quarks to protons may have a line of its own, like water’s boiling line, at densities higher than early universe had, with a sharp jump along it and a critical point at its end. Early universe would then have gone round that end, the smooth way. Colliders smash gold nuclei together at lower and lower energies, making denser drops, to look for the end. The latest measurements show a dip near one collision energy in the shape of the spread of proton numbers: in how often a collision makes far more or far fewer protons than usual. It is a hint of the kind the search looks for, not yet a discovery, and the search goes on.
