Speaker
Description
Weak first-order transitions can exhibit extended pseudo-critical regimes that are notoriously difficult to distinguish from genuine criticality by conventional finite-size scaling. We show that the long-standing apparent criticality of the dilute Baxter—Wu model is instead a manifestation of an extremely slow renormalization-group flow due to a nearly marginal perturbation, ultimately leading to a weak first-order transition. Combining \rev{symmetry analysis} and conformal perturbation theory with tensor-network renormalization, we characterize the ``walking" mechanism by the deformation of the marginal operator spectrum and the beta function of an associated slowly running coupling through quartic order. Our diagnosis extends to the self-dual generalized Baxter—Wu model with distinct interactions on up- and down-pointing triangles, which, as it turns out, follows the same step-scaling function, revealing the local renormalization-group flow structure on both the marginally relevant and irrelevant sides across the four-state Potts point.