second-order transition
Heat a fridge magnet hotter and hotter. At a certain temperature it quietly stops being magnetic — but there is no sudden jolt, no bubbling, no hidden gulp of energy. The magnetism simply fades away smoothly until it is gone. That kind of gentle, no-jump changeover is a second-order, or continuous, transition.
In a second-order transition there is no coexistence of two distinct phases and no latent heat to absorb. Instead the order in the material melts away continuously as you approach the transition point, reaching zero exactly there. Right at that point the material becomes unusually sensitive and restless, with fluctuations of every size flickering through it. Because nothing jumps, the two phases merge seamlessly into one another rather than fighting side by side.
Second-order transitions matter because the special point where they happen — the critical point — shows beautiful universal behavior that turns up across wildly different materials. A common confusion is to think 'continuous' means 'boring' or 'gradual everywhere'. In fact the approach to the transition is dramatic: properties can shoot off toward infinity, just smoothly rather than with a jump.
A piece of iron loses its magnetism in a second-order transition at 770°C, the Curie temperature. If you slowly heat a magnet through that point, its pull does not snap off all at once; it weakens more and more, dwindling smoothly to nothing right at the critical temperature.
Iron's magnetism fades smoothly to zero at its Curie temperature — a textbook second-order transition.
Like 'first-order', the label 'second-order' is old mathematical terminology, not a quality grade. Today physicists more often just say 'continuous transition', because what really sets these apart is the absence of latent heat and the smooth, jump-free changeover.