Continuum field theories emerge as low-energy limits of discrete lattice theories
Multiple studies demonstrate that continuum field theories and effective spacetime dynamics naturally emerge as low-energy or coarse-grained limits of underlying discrete lattice and network theories.
The claim is a standard physics principle well-represented in the provided literature, where lattice models, discrete networks, and quantum crystals are regularly coarse-grained via renormalization group or effective field theory techniques to yield continuum limits.
Dong J, Sommer OE, Soejima T, Parker DE, Vishwanath A. Phonons in electron crystals with Berry curvature.. 2025. https://doi.org/10.1073/pnas.2515532122
Paper 0 derives a low-energy effective continuum phonon theory from microscopic quantum crystal lattice models.
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Vaillant M, Scott TC. A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics.. 2026. https://doi.org/10.3390/e28050544
Paper 2 proposes a microphysical completion for dilatonic gravity by coarse-graining a discrete relational network.
Calliari G, Ott R, Pichler H, Zache TV. Field Digitization Scaling in a Z_{N}⊂U(1) Symmetric Model.. 2026. https://doi.org/10.1103/x164-8n1w
Paper 4 utilizes effective field theory and renormalization group flow to analyze field digitization scaling from discrete lattice models to continuous U(1) field theories.
Hannan M. Spacetime and Yang–Mills from String Flux: A Background-Independent, Flux-First Framework Unifying Emergent Gravity and Emergent Gauge Theory, with Renormalization-Group Analysis, String-Theoretic Embedding, and First Numerical Tests. 2026. https://doi.org/10.21203/rs.3.rs-10232321/v2
Paper 9 constructs an effective statistical field theory where classical spacetime geometry and gravity emerge from a discrete flux-tube network via renormalization group coarse-graining.
Hannan M. Spacetime Emergence from Flux-Tube Connectivity: A Flux-First Framework, Renormalization-Group Analysis, String-Theoretic Embedding, and First Numerical Tests. 2026. https://doi.org/10.21203/rs.3.rs-10232321/v1
Paper 10 (identical to 9) similarly derives continuous spacetime geometry and dynamics from the connectivity of a microscopic discrete lattice substrate.
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