Speaker
Description
In the critical regime of statistical-mechanical systems, thermodynamic quantities follow power laws as functions of a control parameter due to the effective interaction of the system at all scales. This universal behavior is associated with scale invariance and, in many cases, extends to conformal invariance, that is, invariance under the most general group of transformations that preserve angles, which in turn imposes additional constraints on the theory.
The functional renormalization group provides an appropriate framework to study this regime, and the derivative expansion is one of its most successful approximation schemes. At finite order, however, the derivative expansion does not exactly preserve conformal invariance, leading to violations of the corresponding Ward identities.
In this work, we study these violations in the three-dimensional Ising universality class, described by an effective scalar $\phi^4$ theory, within the derivative expansion of the functional renormalization group up to order $O(\partial^4)$, including composite operators. This makes it possible to derive new conformal constraints and to follow how the same constraint evolves at successive orders of the approximation scheme, providing a test of the convergence of the derivative expansion from the viewpoint of symmetry restoration.
We also show that conformal information can be used directly, not only as a diagnostic of the approximation, but also to improve it. Incorporating conformal constraints directly into the truncation leads to a significant improvement in the estimate of critical exponents and to a reduced residual dependence on the regulator. This highlights the connection between regulator optimization, conformal symmetry, and the accuracy of functional renormalization group approximations.
| Affiliation | Universidad de la República (UdelaR) |
|---|---|
| Career status | Student |