universality class
Imagine sorting thousands of recipes not by their ingredients, but by how they ultimately taste. You would find that wildly different ingredient lists can land in the same flavor family. Physicists do something similar with phase transitions: they sort utterly different materials into families based on how they behave at their critical points. Each such family is a universality class.
A universality class is a group of systems that share identical critical exponents and the same critical behavior, even though their microscopic makeup is entirely different. What decides which class a system belongs to is not its atoms but a few coarse, structural facts: how many spatial dimensions it lives in, how many independent directions its order parameter can point, and the range of its interactions. Get those right, and a magnet, a fluid and an alloy can all share one membership card.
Universality classes matter because they bring breathtaking order to the chaos of materials: instead of an endless catalog of unique behaviors, there is a small number of classes, each with its own fixed set of exponents. The honest caveat is that membership is decided by symmetry and dimension, not by what 'looks similar' — two materials that seem alike can fall into different classes, while two that seem unrelated can share one. It is the deep structure, not the surface appearance, that sorts them.
The boiling of an ordinary fluid at its critical point and the demagnetizing of a simple magnet belong to the same universality class — the famous three-dimensional Ising class. They are governed by exactly the same critical exponents, so a measurement on water near its critical point and a measurement on a uniaxial (Ising-type) magnet near its Curie point yield matching numbers.
Boiling water and a demagnetizing uniaxial (Ising-type) magnet sit in the same universality class, sharing identical exponents.
In the language of the renormalization group, a universality class is simply the set of all systems that flow to the same fixed point under repeated coarse-graining. That shared destination, not their starting ingredients, is what binds the members of a class together.