Critical behavior and scaling in trapped systems

TL;DR

This paper investigates the critical behavior of particle systems confined by trapping potentials, introducing a trap-size scaling framework characterized by a nontrivial exponent, supported by numerical simulations of lattice gas models.

Contribution

It develops a trap-size scaling theory for confined critical systems, extending finite-size scaling concepts with a new trap critical exponent theta.

Findings

Trap-size scaling describes critical behavior in trapped systems.

Numerical results support the proposed scaling scenario.

The trap critical exponent theta depends on the universality class and trap details.

Abstract

We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling theory, with a nontrivial trap critical exponent theta, which describes how the correlation length scales with the trap size l, i.e., $\xi\sim l^\theta$ at the critical point. theta depends on the universality class of the transition, the power law of the confining potential, and on the way it is coupled to the critical modes. We present numerical results for two-dimensional lattice gas (Ising) models with various types of harmonic traps, which support the trap-size scaling scenario.