A critical point is the specific temperature and pressure where distinct phases of matter become indistinguishable.Imagine a kettle with boiling water. Normally, when water turns into steam, you can see bubbles and bubbling. But if you heat water under high pressure, you can reach a state where water and steam become completely indistinguishable — this is the critical point. At this point, liquid and gas merge into a single state, like a thick fog, but without a surface boundary. It's similar to how, in the morning, the air is so saturated with moisture that dew droplets and air merge into one whole.
The critical point was discovered by Charles Cagniard de la Tour in 1822, but systematically studied by Thomas Andrews in 1869. Andrews showed that for each gas there is a temperature above which it cannot be liquefied. In 1873, Johannes van der Waals proposed an equation of state for real gas that for the first time explained the existence of a critical point based on molecular forces. In the 20th century, Landau developed the theory of second-order phase transitions, and Wilson applied renormalization group to describe universal critical phenomena.
From a microscopic perspective, the critical point is the result of a balance between intermolecular attraction, which tends to condense the substance, and thermal motion, which tends to expand it. At the critical temperature, the attraction energy equals the thermal energy, and the phase boundary disappears. This is described by the van der Waals equation, which includes parameters a and b. At the critical point, compressibility tends to infinity, and the correlation length of fluctuations becomes macroscopic, leading to critical opalescence. In modern understanding, critical phenomena are universal and do not depend on system details, but are determined only by the dimensionality of space and the symmetry of the order parameter, as described by renormalization group theory.
Did you know that at the critical point, water can simultaneously wet and not wet the walls of the container? The difference between liquid and steam disappears, and surface tension vanishes, so the liquid stops forming droplets.
| P_c | variable | Critical pressure — pressure pascal |
| v_c | variable | Critical molar volume — molar volume cubic metre per mole |
| T_c | variable | Critical temperature — temperature kelvin |
| U | variable | Effective pairing interaction strength — coupling constant joule metre cubed |
| χ | variable | Pair susceptibility (response function) — susceptibility per joule per metre cubed |
| ω | variable | Frequency (Matsubara or real) — angular frequency per second |
| E_c | variable | Critical energy — energy joule |
| m_a | variable | Axion mass — mass kilogram |
| ω_pl | variable | Plasma frequency — angular frequency radian per second |
| B_perp | variable | Perpendicular magnetic field strength — magnetic field strength tesla |
| g_aγ | variable | Axion-photon coupling constant — coupling constant inverse gev |
| p_1 | variable | Pre-shock pressure — pressure pascal |
| p_2 | variable | Post-shock pressure — pressure pascal |
| \gamma | variable | Adiabatic index (ratio of specific heats) — adiabatic index |















