Marginal Operator Deformations and Pseudocriticality in Baxter--Wu Models

Abstract

Weak first-order transitions can exhibit extended pseudocritical scaling regimes that mimic genuine criticality. We show that the long-debated apparent criticality of the dilute Baxter--Wu model arises from a marginally relevant renormalization-group flow, which ultimately drives the system into a first-order regime with phase coexistence. By integrating conformal perturbation theory with symmetry-resolved tensor-network level spectroscopy, we parameterize a slowly running coupling in a numerically accessible form and construct a generic flow-based diagnostic. The renormalization-group trajectories of the dilute and self-dual Baxter--Wu models under marginal operator deformations collapse onto the multicritical phase diagram of the dilute four-state Potts model, exposing the flow structure on both the marginally relevant and irrelevant sides of the Potts point.