Scaling in the vicinity of the four-state Potts fixed point

TL;DR

This paper investigates a generalized Baxter-Wu model near the four-state Potts fixed point, analyzing how different couplings influence critical behavior and logarithmic corrections, confirming renormalization theory predictions.

Contribution

It provides a detailed finite-size analysis of how various couplings affect the model's proximity to the four-state Potts fixed point and the associated critical phenomena.

Findings

Pure Baxter-Wu model exhibits four-state Potts critical behavior without logarithmic corrections.

Introducing real couplings leads to first-order transition behavior.

Complex couplings induce logarithmic corrections similar to the four-state Potts model.

Abstract

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.