Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

TL;DR

This study investigates the directional-ordering transition in 2D classical and quantum compass models using Monte Carlo simulations, introduces improved algorithms and boundary conditions, and provides new insights into finite-size scaling and critical temperature estimation.

Contribution

It presents an improved Monte Carlo algorithm and boundary conditions that eliminate finite-size scaling issues in the compass model, enhancing the accuracy of critical temperature estimates.

Findings

Strong anomalous finite-size scaling under periodic boundary conditions.

Alternative boundary conditions remove finite-size scaling problems.

Identified a one-dimensional magnetic ordering tendency with large correlation length.

Abstract

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.