Gradient flow method provides a practical framework for implementing Renormalization Group (RG) transformations on the lattice, commonly referred to as the Gradient Flow Renormalization Group (GFRG). In this work, we investigate the RG flow of the two-dimensional scalar $\phi^4$ theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.Gradient flow method provides a practical framework for implementing Renormalization Group (RG) transformations on the lattice, commonly referred to as the Gradient Flow Renormalization Group (GFRG). In this work, we investigate the RG flow of the two-dimensional scalar $\phi^4$ theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.

International Symposium on Lattice Field Theory (LATTICE)Jun 29, 20260 citations

Basic Issues of Renormalization Group (RG) Theory

WORLD SCIENTIFIC eBooksSep 11, 20180 citations

Basic Issues of Renormalization Group (RG) Theory

U. Köbler, A. Hoser

Springer series in materials scienceSep 24, 20090 citations

Refined half-integer condition on RG flows

Ken Kikuchi

Renormalization group flows are constrained by symmetries. Traditionally, we have made the most of 't Hooft anomalies associated to the symmetries. The anomaly is mathematically part of the data for the monoidal structure on symmetry categories. The symmetry categories sometimes admit additional structures such as braiding. It was found that the additional structures give further constraints on renormalization group flows. One of these constraints is the half-integer condition. The condition claims the following. Braidings are characterized by conformal dimensions. A symmetry object $c$ in a braided symmetry category surviving all along the flow thus has two conformal dimensions, one in ultraviolet $h_c^\text{UV}$ and the other in infrared $h_c^\text{IR}$ . In a renormalization group flow with a renormalization group defect, they add up to a half-integer $h_c^\text{UV}+h_c^\text{IR}\in\frac12\mathbb Z$ . We find a necessary condition for the sum to be half-integer. We solve some flows with the refined half-integer condition.Renormalization group flows are constrained by symmetries. Traditionally, we have made the most of 't Hooft anomalies associated to the symmetries. The anomaly is mathematically part of the data for the monoidal structure on symmetry categories. The symmetry categories sometimes admit additional structures such as braiding. It was found that the additional structures give further constraints on renormalization group flows. One of these constraints is the half-integer condition. The condition claims the following. Braidings are characterized by conformal dimensions. A symmetry object $c$ in a braided symmetry category surviving all along the flow thus has two conformal dimensions, one in ultraviolet $h_c^\text{UV}$ and the other in infrared $h_c^\text{IR}$. In a renormalization group flow with a renormalization group defect, they add up to a half-integer $h_c^\text{UV}+h_c^\text{IR}\in\frac12\mathbb Z$. We find a necessary condition for the sum to be half-integer. We solve some flows with the refined half-integer condition.

arXiv:2602.12085Feb 12, 20260 citations

Introduction to the Renormalization Group

Shang-keng Ma

WORLD SCIENTIFIC eBooksAug 1, 19931 citation

Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

Stefan Alexander Maier, Andreas Eberlein, Carsten Honerkamp A

We present a functional renormalization group (fRG) formalism for interacting fermions on lattices that captures the flow into states with commensurate spin-density-wave order. During the flow, the growth of the order parameter is fed back into the flow of the interactions and all modes can be integrated out. This extends previous fRG flows in the symmetric phase that run into a divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering scale. We use the corresponding Ward identity to check the accuracy of the results. We apply our method to a model with two Fermi pockets that have perfect particle-hole nesting. The results obtained from the fRG are compared with those in random-phase approximation.We present a functional renormalization group (fRG) formalism for interacting fermions on lattices that captures the flow into states with commensurate spin-density-wave order. During the flow, the growth of the order parameter is fed back into the flow of the interactions and all modes can be integrated out. This extends previous fRG flows in the symmetric phase that run into a divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering scale. We use the corresponding Ward identity to check the accuracy of the results. We apply our method to a model with two Fermi pockets that have perfect particle-hole nesting. The results obtained from the fRG are compared with those in random-phase approximation.

arXiv:1406.2906Physical Review BJul 29, 201417 citations

Lattice study of RG flow in 2D

\phi^4

theory

\phi^4

theory in the vicinity of criticality. To address the problem of critical slowing down near the critical point, we employ Conditional Normalizing Flows (CNFs) to efficiently generate field configurations in the critical region. This combination of GFRG and CNFs enables a controlled non-perturbative study of critical behaviour and fixed-point structure.

c

in a braided symmetry category surviving all along the flow thus has two conformal dimensions, one in ultraviolet

h_c^\text{UV}

and the other in infrared

h_c^\text{IR}

. In a renormalization group flow with a renormalization group defect, they add up to a half-integer

h_c^\text{UV}+h_c^\text{IR}\in\frac12\mathbb Z

. We find a necessary condition for the sum to be half-integer. We solve some flows with the refined half-integer condition.