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The tricritical Ising CFT and conformal bootstrap
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The tricritical Ising CFT and conformal bootstrap
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The tricritical Ising CFT is the IR fixed-point of $\lambda\phi^6$ theory. It can be seen as a one-parameter family of CFTs connecting between an $\varepsilon$-expansion near the upper critical dimension 3 and the exactly solved minimal model in $d=2$. We review what is known about the tricritical Ising CFT, and study it with the numerical conformal bootstrap for various dimensions. Using a mixed system with three external operators $\{\phi\sim\sigma,\phi^2\sim \epsilon,\phi^3\sim\sigma'\}$, we find three-dimensional "bootstrap islands" in $d=2.75$ and $d=2.5$ dimensions consistent with interpolations between the perturbative estimates and the 2d exact values. In $d=2$ and $d=2.25$ the setup is not strong enough to isolate the theory. This paper also contains a survey of the perturbative spectrum and a review of results from the literature.
Forward citations
Cited by 5 Pith papers
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Six-loop beta-function graphs for general ϕ⁶ theory in 3d are recalculated (differing from Hager, agreeing with recent work), with large-N eight-loop results, O(ε³) exponents, and gradient-flow linear relations.
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On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions
The d→2 Wilson-Fisher limit is proposed to be strictly larger than the 2d Ising CFT, which emerges as a unitary subsector after negative-multiplicity operators cancel exactly.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Recalculation of individual six-loop graph contributions to the beta function in 3d phi^6 theory with arbitrary potential, plus large-N eight-loop terms and O(epsilon^3) critical exponents at the O(N) fixed point.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Recalculation of individual six-loop graph contributions to the β-function in 3d φ⁶ theory with arbitrary potential, plus large-N eight-loop diagrams and O(ε³) critical exponents at the O(N) fixed point.
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