Functional renormalization group in an external field: constant field versus constant order parameter
Abstract
Renormalization group (RG) flows for systems subject to an external field can be derived either by fixing the field or by fixing the conjugate order parameter. We show how to implement these boundary conditions within the functional renormalization group approach. We derive and compare the corresponding flow equations for ϕ4 theory and show that some scaling variables and scaling exponents associated with the linearized flow of the relevant three-point vertex in the vicinity of the Ising fixed point depend on the boundary conditions. We also discuss the effect of elasticity on Ising criticality. In this case two of the fixed points (namely the renormalized Ising fixed point and the spherical fixed point) obtained for constant strain are shifted to physically inaccessible regimes of parameter space when we perform the RG at constant stress.
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BibTeX
@misc{rothkirch2026functional,
title = {{Functional renormalization group in an external field: constant field versus constant order parameter}},
author = {Julia von Rothkirch and Andreas Rückriegel and Peter Kopietz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03365},
eprint = {2610.03365},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03365},
}
RIS
TY - UNPB
TI - Functional renormalization group in an external field: constant field versus constant order parameter
AU - Julia von Rothkirch
AU - Andreas Rückriegel
AU - Peter Kopietz
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03365
UR - https://arxiv.org/abs/2610.03365
AB - Renormalization group (RG) flows for systems subject to an external field can be derived either by fixing the field or by fixing the conjugate order parameter. We show how to implement these boundary conditions within the functional renormalization group approach. We derive and compare the corresponding flow equations for ϕ^4 theory and show that some scaling variables and scaling exponents associated with the linearized flow of the relevant three-point vertex in the vicinity of the Ising fixed point depend on the boundary conditions. We also discuss the effect of elasticity on Ising criticality. In this case two of the fixed points (namely the renormalized Ising fixed point and the spherical fixed point) obtained for constant strain are shifted to physically inaccessible regimes of parameter space when we perform the RG at constant stress.
ER -