GOD Theory IX: Critical Exponents of Phase Transitions from the SkinnerTorrado Algebra
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2026
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| _version_ | 1866901720473272320 |
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| author | Torrado-Cano, Francisco |
| author_facet | Torrado-Cano, Francisco |
| contents | <p>We derive the critical exponents of the three-dimensional Ising universality class<br>as exact rational numbers from the SkinnerTorrado curvature coecients C(n) =<br>Γ(1 + n)<br>2/Γ(1 + 2n) established in Articles 1a1b [1, 2].<br>Three independent predictions are obtained algebraically from the four known<br>enrollment subspaces of M:<br>η3D =C(3)^3/(C(1)^3 · C(2)^2)=9/250= 0.0360, (I)<br>ν3D =C(3)^3/(C(1) · C(2)^2 · C(4)) =7!/20^3=63/100= 0.63, (II)<br>β3D =C(4)^2/(C(1)^2 · C(3)^2)=16/49= 0.326531 . . . (III)<br>These agree with the state-of-the-art conformal bootstrap determinations [9] to<br>0.005% (ν), 0.034% (β), and 0.82% (η). All remaining exponents follow by standard<br>scaling relations and are likewise exact rationals: γ = 30933/25000, α = 11/100,<br>δ = 1241/259.<br>We show that the exact critical exponents of the two-dimensional Ising model<br>(Onsager solution, 1944) are recovered as powers of C(1) = 1/2: η2D = C(1)2 = 1/4,<br>ν2D = C(0) = 1, β2D = C(1)3 = 1/8. Mean-eld exponents (d ≥ 4) are similarly<br>recovered: νMF = βMF = C(1) = 1/2, ηMF = 0.<br>We then construct the complete thermodynamic framework of GOD Theory:<br>phase transitions as enrollment transitions of M; the Carnot cycle as a closed trajectory in enrollment space; adiabatic compression as topological compactication<br>of a fold; and the connection between tokamak disruptions (Article 3, [3]) and classical phase transitions via the common structure of the SkinnerTorrado algebra at<br>enrollment thresholds.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19599917 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | GOD Theory IX: Critical Exponents of Phase Transitions from the SkinnerTorrado Algebra Torrado-Cano, Francisco critical exponents, Ising model, phase transitions, universality, Skinner Torrado algebra, fractal manifold, Carnot cycle, thermodynamics, GOD Theory <p>We derive the critical exponents of the three-dimensional Ising universality class<br>as exact rational numbers from the SkinnerTorrado curvature coecients C(n) =<br>Γ(1 + n)<br>2/Γ(1 + 2n) established in Articles 1a1b [1, 2].<br>Three independent predictions are obtained algebraically from the four known<br>enrollment subspaces of M:<br>η3D =C(3)^3/(C(1)^3 · C(2)^2)=9/250= 0.0360, (I)<br>ν3D =C(3)^3/(C(1) · C(2)^2 · C(4)) =7!/20^3=63/100= 0.63, (II)<br>β3D =C(4)^2/(C(1)^2 · C(3)^2)=16/49= 0.326531 . . . (III)<br>These agree with the state-of-the-art conformal bootstrap determinations [9] to<br>0.005% (ν), 0.034% (β), and 0.82% (η). All remaining exponents follow by standard<br>scaling relations and are likewise exact rationals: γ = 30933/25000, α = 11/100,<br>δ = 1241/259.<br>We show that the exact critical exponents of the two-dimensional Ising model<br>(Onsager solution, 1944) are recovered as powers of C(1) = 1/2: η2D = C(1)2 = 1/4,<br>ν2D = C(0) = 1, β2D = C(1)3 = 1/8. Mean-eld exponents (d ≥ 4) are similarly<br>recovered: νMF = βMF = C(1) = 1/2, ηMF = 0.<br>We then construct the complete thermodynamic framework of GOD Theory:<br>phase transitions as enrollment transitions of M; the Carnot cycle as a closed trajectory in enrollment space; adiabatic compression as topological compactication<br>of a fold; and the connection between tokamak disruptions (Article 3, [3]) and classical phase transitions via the common structure of the SkinnerTorrado algebra at<br>enrollment thresholds.</p> |
| title | GOD Theory IX: Critical Exponents of Phase Transitions from the SkinnerTorrado Algebra |
| topic | critical exponents, Ising model, phase transitions, universality, Skinner Torrado algebra, fractal manifold, Carnot cycle, thermodynamics, GOD Theory |
| url | https://doi.org/10.5281/zenodo.19599917 |