# Critical behavior of itinerant fermions - role of finite size effects

## TL;DR

This paper investigates how finite size effects influence the critical behavior of itinerant fermions near a q=0 critical point, explaining discrepancies in recent QMC results and highlighting implications for small fermionic systems.

## Contribution

It demonstrates that finite size effects significantly alter critical behavior for z=3 systems, reconciling QMC findings with theoretical expectations.

## Key findings

- Finite size effects are strong for z=3 criticality.
- Finite size effects can explain discrepancies in QMC results.
- Implications for small fermionic systems like magnetic nanoparticles.

## Abstract

We study the role of finite size effects on a metallic critical behavior near a q = 0 critical point and compare the results with the recent extensive quantum Monte-Carlo (QMC) study [Y. Schattner et al, PRX 6, 0231028]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with dynamical exponent z = 3. We show that finite size effects are particularly strong for z = 3 criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite size effects into account, the QMC results can be explained within z = 3 theory. Our results also have implications for small interacting fermionic systems, such as magnetic nanoparticles.