A continuous phase transition where the order parameter changes smoothly to zero.A second-order phase transition is a continuous transition between phases of matter where the order parameter—a quantity that distinguishes the phases—goes to zero smoothly at the critical point. Unlike first-order transitions (like boiling water), there is no latent heat and no coexistence of phases. Instead, fluctuations of the order parameter become large and correlated over long distances, leading to universal behavior near the critical point. Examples include the ferromagnetic transition (where magnetization vanishes) and the superconducting transition in zero magnetic field.
The modern theory of second-order phase transitions was developed in the 1960s and 1970s, with key contributions from Lev Landau (Landau theory), Kenneth Wilson (renormalization group), and Leo Kadanoff (scaling ideas). Wilson's work earned him the 1982 Nobel Prize in Physics.
As the system approaches the critical temperature, the free energy landscape flattens, so the order parameter can fluctuate strongly. These fluctuations have a characteristic length scale (correlation length) that diverges at the critical point. This divergence leads to scale invariance: the system looks the same at all length scales, which is why critical exponents are universal across very different systems. The transition is driven by the competition between energy (which favors order) and entropy (which favors disorder).
Second-order transitions are exploited in magnetic storage (where the transition temperature determines data stability), in superconducting magnets, and in understanding critical phenomena in diverse fields from cosmology to biology.
Near a second-order phase transition, the system becomes so sensitive that its response to external fields (like magnetic susceptibility) can diverge to infinity, a phenomenon called critical opalescence in fluids.









