ordreparameter

An ordreparameter is a quantity that characterizes the degree of order in a system and serves to distinguish different phases, especially across a phase transition. In English-language literature the term is usually written as order parameter; in some contexts, particularly in French-language sources, it is referred to as paramètre d'ordre. The concept captures spontaneous symmetry breaking: typically a nonzero value in one phase and a zero value in another when external fields are absent.

Common examples include the magnetization M in a ferromagnet (nonzero below the Curie temperature, zero above), and the complex superfluid order parameter psi in superconductors or bosonic superfluids. Other instances are the density difference between liquid and gas, or the staggered magnetization in antiferromagnets. Order parameters can be scalar, vector, or tensor quantities and may vary in space, forming an order-parameter field phi(r).

In theoretical treatments such as Landau theory, the free energy is expressed as a function of the order parameter and sometimes its gradients. Minimization yields the equilibrium state, and the behavior of the order parameter near a transition determines the transition’s character: continuous (second-order) or discontinuous (first-order). The concept also extends to finite systems, where true long-range order is replaced by crossovers; finite-size scaling describes how the order parameter approaches the thermodynamic limit.

Beyond conventional magnets and superconductors, order parameters play a role in percolation, where the fraction of sites in the spanning cluster can serve as an order parameter, and in various gauge or topological transitions. In experiments, the order parameter is often inferred from measurable proxies such as magnetization, superfluid density, or optical/structural order parameters.

In sum, the ordreparameter is a central diagnostic tool in condensed matter physics, statistical mechanics, and related fields, linking symmetry, phase structure, and critical phenomena.