Dimension-created constrained phases and fixed-point bifurcations in the complete four-colour Ashkin–Teller model

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22848959
Primary Topic
Physics of Superconductivity and Magnetism
Type
preprint
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preprint

Dimension-created constrained phases and fixed-point bifurcations in the complete four-colour Ashkin–Teller model

Egemen Ekinci
Zenodo (CERN European Organization for Nuclear Research)
Physics of Superconductivity and Magnetism
preprint

Dimension-created constrained phases and fixed-point bifurcations in the complete four-colour Ashkin–Teller model

Egemen Ekinci
preprint en

Abstract

Preprint of the manuscript "Dimension-created constrained phases and fixed-point bifurcations in the complete four-colour Ashkin–Teller model", deposited together with the complete reproducibility package for the study. We introduce the complete permutation-symmetric four-colour Ashkin–Teller model, whose nearest-neighbour Hamiltonian contains independent two-, four-, six-, and eight-spin interactions. Its 16-state transfer matrix reduces exactly to five radial weights under a binary Krawtchouk transform. We solve the resulting b=3 real-space renormalization-group recursion in two and three dimensions; it is exact on the associated diamond hierarchical lattice and is the ordinary Migdal–Kadanoff approximation on Bravais lattices. Five ordered phases occur in d=2. In d=3, two additional phases, C1 and C3, occur in 22 of 25 coupling sections and occupy 20.3493% of the sampled global atlas. They are not ordinary subgroup or coset phases: exact compatibility counting identifies them as non-coset constrained phases with staggered four-colour-product order and certifies their d=3 residual entropy within [1.151635164996, 1.151635172152]. A general N-colour character identity shows that every pure odd-mismatch shell enforces staggered full-product order on a bipartite lattice. CORRECTION (version 3.0.0, 19 September 2026). The description of C1 and C3 above as non-coset constrained phases is corrected. The single mismatch shells that support them are indeed not cosets, but they are not closed under the renormalization step and therefore are not constrained supports: one threefold sum already escapes, since 1000 + 0100 + 0010 = 1110 has mismatch 3, and the closure of either single shell is the full odd coset. C1 and C3 are limit points inside the odd-coset face, distinguished by which shell carries the dominant weight, which is consistent with the parameterisation by r = t1/t3 in section 6 of the paper. No numerical result changes: the phases, their staggered four-colour-product order, the certified entropy interval, the dimension-created folds, the fixed-point census and the cubic corroboration are all unaffected, and the X, Q+ and Q- assignments were already correct. Details in CORRECTION_to_quadrupled_AT.md, added to this version, and in the companion classification note doi:10.5281/zenodo.22848906, which proves that a non-coset constrained support cannot occur at any colour count. Two distinct dimension-created folds organize the new topology: a finite fixed-point pair born at d_SN = 2.5601299591, and a separate exactly reduced odd-sector fold at d* = 2.8908652348 that creates the C1/C3 sinks and separators. A stratified multistart search finds 29 finite fixed points in d=2 and 37 in d=3. Free-energy derivatives were evaluated on 2,087 refined interfaces, and an independent periodic-cubic Metropolis test at L=6,8,10,12 corroborates the constraint signature. Contents: the manuscript and the supplement (PDF and DOCX), and Quadrupled_AT_Reproducibility_Package.tar.gz, which contains the physical 16-state renormalization-group implementation, the global phase-atlas data, the exact constraint and entropy certificates, the dimensional-bifurcation analyses, the transition-order diagnostics, the periodic-cubic finite-size corroboration, the analysis scripts, and the test suite needed to reproduce every number in the paper. A portable SHA-256 checksum is supplied alongside the archive. Version 2.0.0 adds the manuscript and supplement to the version 1.0.0 code and data package. Preprint. Not peer reviewed. This work was produced with substantial AI assistance (Claude, Anthropic). The author takes full responsibility for the content.

Zenodo (CERN European Organization for Nuclear Research)
Physics of Superconductivity and Magnetism
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