O(N) Universality Class

The O(N) universality class describes a category of physical systems with N-component variables, like spins or vectors, that exhibit similar behavior near critical points, such as phase transitions. These models share common critical exponents and scaling laws, regardless of microscopic details. For example, when N=1, it relates to magnetic materials like ferromagnets; for N=2, it models superfluid helium; and for N=3, it describes isotropic magnets. The "O(N)" notation refers to the symmetry of the system under rotations in N-dimensional space. This universality simplifies understanding critical phenomena across diverse systems by grouping them based on their symmetry and dimensionality.