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Upper critical dimension of the 3-state Potts model

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arxiv 2210.09091 v3 pith:VJ4FZH6H submitted 2022-10-17 hep-th cond-mat.stat-mechcond-mat.str-el

Shai M. Chester , Ning Su This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-el
keywords criticalfixedcritmodeltextdimensionexponentspoint
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abstract

We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal models, and so are exactly solvable. For $d>2$, however, strong coupling makes them difficult to study and there is no consensus on the value of $d_\text{crit}$. We use the numerical conformal bootstrap to compute critical exponents of both the critical and tricritical fixed points for general $d$. In $d=2$ our results match the expected values, and as we increase $d$ we find that the critical exponents of each fixed point get closer until they merge near $d_\text{crit}\lesssim 2.5$.

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Cited by 4 Pith papers

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  1. Self-dual $S_3$ gauge theory in 2+1d: lattice model and topological phase transitions

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    A new sign-problem-free lattice Hamiltonian realizes the S3 quantum double with electric-magnetic duality as translation, yielding a tetracritical Ising boundary and three predicted topological transitions.

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    First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.

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    Conformal bootstrap bounds for U(1)-charged scalars in 3d are saturated by the CP^2 model's large-N and lattice predictions, suggesting the CP^2 deconfined quantum critical point is a conformal field theory.

  4. Microscopic study of 3D Potts phase transition via Fuzzy Sphere Regularization

    cond-mat.stat-mech 2025-01 conditional novelty 6.0 of 10

    A fuzzy-sphere model of the 3D 3-state Potts transition shows approximate conformal symmetry and a drifting subleading singlet dimension near 3, suggesting a weakly first-order transition with pseudo-critical behavior.

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