Scaling laws for Ising models near T_c¶
Kadanoff, L. P. (1966). Scaling laws for Ising models near T_c. Physics Physique Fizika, 2(6), 263-272.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Criticality
- It separates three regimes (ordered, critical, disordered) and names what is distinctive about the middle: the absence of any characteristic scale and the unboundedness of correlations and responses, a structural reading Kadanoff (1966) made explicit in his block-spin construction that became the conceptual backbone of the renormalization group.
This sourceIntroduces the block-spin construction—dividing the Ising lattice into cells large compared with the lattice spacing but small compared with the correlation length—that became the conceptual backbone of the renormalization group and the explicit structural reading the marker attributes to Kadanoff.
- It separates three regimes (ordered, critical, disordered) and names what is distinctive about the middle: the absence of any characteristic scale and the unboundedness of correlations and responses, a structural reading Kadanoff (1966) made explicit in his block-spin construction that became the conceptual backbone of the renormalization group.
- Renormalization
- In Kadanoff's 1966 treatment,
This sourceIntroduces renormalization group approach to equilibrium critical phenomena; shows that equilibrium phase transitions exhibit emergent scaling and that ensemble-dependent properties vanish only in thermodynamic limit, clarifying finite-size breakdown of equivalence.
- In Kadanoff's 1966 treatment,
- Scale Invariance
- The scaling exponent α (or β, γ, ν in critical phenomena) governs how observables transform and classifies systems into universality classes
This sourceIntroduces renormalization group approach to equilibrium critical phenomena; shows that equilibrium phase transitions exhibit emergent scaling and that ensemble-dependent properties vanish only in thermodynamic limit, clarifying finite-size breakdown of equivalence.
- The scaling exponent α (or β, γ, ν in critical phenomena) governs how observables transform and classifies systems into universality classes
- Scaling and Scale Dependence
- A power law is scale-invariant (the ratio between any two scales holds across the range); the mechanisms causing a power law often are scale-dependent (turbulence in air differs from turbulence in honey), a distinction that Kadanoff (1966) clarified by deriving how block-spin renormalization can preserve a scaling form while the microscopic dynamics change qualitatively across regimes.
This sourceIntroduces renormalization group approach to equilibrium critical phenomena; shows that equilibrium phase transitions exhibit emergent scaling and that ensemble-dependent properties vanish only in thermodynamic limit, clarifying finite-size breakdown of equivalence.
- A power law is scale-invariant (the ratio between any two scales holds across the range); the mechanisms causing a power law often are scale-dependent (turbulence in air differs from turbulence in honey), a distinction that Kadanoff (1966) clarified by deriving how block-spin renormalization can preserve a scaling form while the microscopic dynamics change qualitatively across regimes.
- Thermodynamic Equilibrium
- T4 — Ensemble Equivalence and Finite-Size Effects: Statistical mechanics asserts that microcanonical, canonical, and grand-canonical ensembles are equivalent in the thermodynamic limit (N→∞, V→∞)
This sourceIntroduces renormalization group approach to equilibrium critical phenomena; shows that equilibrium phase transitions exhibit emergent scaling and that ensemble-dependent properties vanish only in thermodynamic limit, clarifying finite-size breakdown of equivalence.
- T4 — Ensemble Equivalence and Finite-Size Effects: Statistical mechanics asserts that microcanonical, canonical, and grand-canonical ensembles are equivalent in the thermodynamic limit (N→∞, V→∞)
- Universality in Critical Phenomena
- T5 — Universality as Deep Insight vs. RG-Scheme Artifact:
This sourceIntroduces renormalization group approach to equilibrium critical phenomena; shows that equilibrium phase transitions exhibit emergent scaling and that ensemble-dependent properties vanish only in thermodynamic limit, clarifying finite-size breakdown of equivalence.
- T5 — Universality as Deep Insight vs. RG-Scheme Artifact:
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