Finite-Size Scaling and Long-Range Interactions

TL;DR

This review explores how long-range interactions that decay as 1/r^{d+σ} influence finite-size scaling in classical and quantum systems, highlighting the theoretical challenges and implications for critical phenomena.

Contribution

It provides a comprehensive analysis of finite-size scaling in systems with long-range interactions, extending classical theories to quantum contexts.

Findings

Finite-size scaling behavior is significantly affected by long-range interactions.

The decay parameter σ determines the universality class of the phase transition.

Quantum systems exhibit distinct finite-size effects compared to classical counterparts.

Abstract

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+\sigma}$, where $d$ is the spatial dimension and the long-range parameter $\sigma>0$. Classical and quantum systems are considered.