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The flow of couplings and operators with resolution scale, expressing how descriptions change under coarse-graining or scale transformations.
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This is an authored directed relation from the source endpoint to the target endpoint.
Renormalization-group evolution is formulated as a scale-parameter flow of couplings or effective actions. This is a dynamical system in theory space, not ordinary time evolution of a material system.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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Renormalization-group equations describe how renormalized couplings and operators change with scale.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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This is an authored directed relation from the source endpoint to the target endpoint.
Renormalization-group flow explains scaling, relevant and irrelevant perturbations, and fixed-point behavior near continuous phase transitions; its conclusions depend on the selected degrees of freedom and coarse-graining scheme.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
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Running couplings solve renormalization-group flow equations.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
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Systems whose coarse-grained couplings flow toward the same infrared fixed point can share critical exponents and scaling functions, while dimensionality, symmetry, interaction range, and conserved dynamics can separate universality classes.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
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