Universal amplitudes in the FSS of three-dimensional spin models

TL;DR

This study uses Monte Carlo simulations to explore the finite-size scaling of correlation lengths in 3D O(n) spin models, revealing a linear relation between FSS amplitudes and scaling dimensions under certain boundary conditions.

Contribution

It demonstrates a universal linear relation between FSS amplitudes and scaling dimensions in 3D spin models with antiperiodic boundary conditions, supported by numerical evidence.

Findings

Linear relation between FSS amplitudes and scaling dimensions

Evidence for universality across different models

Analytical proof for 2D systems with periodic boundary conditions

Abstract

In a MC study using a cluster update algorithm we investigate the finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical O(n) symmetric spin models on a column geometry. For all considered models we find strong evidence for a linear relation between FSS amplitudes and scaling dimensions when applying antiperiodic instead of periodic boundary conditions across the torus. The considered type of scaling relation can be proven analytically for systems on two-dimensional strips with periodic bc using conformal field theory