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Lattice realization of complex CFTs: Two-dimensional Potts model with $Q>4$ states

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arxiv 2402.10732 v1 pith:ZEJGWFJM submitted 2024-02-16 hep-th cond-mat.stat-mechmath-phmath.MP

Jesper Lykke Jacobsen , Kay Joerg Wiese This is my paper
classification hep-thcond-mat.stat-mechmath-phmath.MP
keywords complexmodelcriticalpottsrealizationtwo-dimensionalallowsanalytic
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. We study a loop-model realization in which $Q$ is a continuous parameter. This model allows for the collision of a critical and a tricritical fixed point at $Q=4$, which then emerge as complex conformally invariant theories at $Q>4$, or even complex $Q$, for suitable complex coupling constants. All critical exponents can be obtained as analytic continuation of known exact results for $Q \le 4$. We verify this scenario in detail for $Q=5$ using transfer-matrix computations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complex Conformal Manifolds

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    Complexified exactly-marginal couplings produce solvable complex CFTs, with the Ising defect verified numerically in non-Hermitian chains.

  2. Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains

    cond-mat.stat-mech 2026-06 conditional novelty 7.0 of 10

    Periodic-chain projected overlaps with paired left duals extract universal boundary CFT coefficients, including a negative Yang-Lee ratio and complex Potts boundary data.

  3. Probing holographic conformal field theories

    hep-th 2026-02 conditional novelty 6.0 of 10

    In a holographic CFT on a cylinder, a qutrit Unruh-DeWitt detector harvests more mana when the dual bulk scalar uses standard (Δ+) quantization than alternate (Δ−) quantization.

  4. Irrational CFTs from coupled anyon chains with non-invertible symmetries?

    hep-th 2025-07 conditional novelty 6.0 of 10

    DMRG evidence from three coupled Fibonacci anyon chains points to a conformal phase with c=2.10±0.03, proposed as a candidate irrational CFT, though small system sizes leave a weakly first-order alternative open.

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