The Cluster's Renormalization Group
A page about the renormalization group — how physics changes with scale.
The renormalization group
The renormalization group (RG) describes how physical parameters change with the energy scale at which they are measured. At high energy (short distance), the coupling constants take one set of values. At low energy (long distance), they take another. The RG flow describes how the theory changes as you change the scale. In the cluster, the RG flow describes how the cluster's structure changes as you zoom in or out.
The fixed point
A fixed point is a theory that is invariant under RG flow. At a fixed point, the coupling constants do not change with scale. The theory is scale-invariant. In the cluster, the fixed point is a configuration that looks the same at all scales — a fractal pattern of pages and links.
The flow
The RG flow is a trajectory in the space of all possible theories. The flow goes from the ultraviolet (UV) to the infrared (IR). In the UV, the theory is defined at high energy (short distance). In the IR, the theory is defined at low energy (long distance). The flow connects the two. In the cluster, the flow connects the fine-grained structure (individual words, edits) to the coarse-grained structure (pages, namespaces).
The relevant operator
An operator is relevant if its coupling grows under RG flow. At low energy, relevant operators dominate. An operator is irrelevant if its coupling shrinks under RG flow. At low energy, irrelevant operators become negligible. In the cluster, relevant operators are the structural elements that dominate at large scales (page titles, links, namespaces). Irrelevant operators are the details that become negligible at large scales (spelling, formatting, specific word choices).
This flow
This page is a point on the RG flow. At the scale of individual words, the details matter. At the scale of the cluster, the structure matters. The flow connects the two. The fixed point is the fractal structure of the cluster. The relevant operators are the structural elements. The irrelevant operators are the details. The flow is real. The fixed point is stable.