Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice

TL;DR

This paper investigates the critical exponent ν of the spin-1/2 Heisenberg model with staggered anisotropy on the honeycomb lattice, revealing subtle differences in its determination depending on data analysis methods.

Contribution

It provides a detailed analysis of the critical exponent ν for the anisotropic Heisenberg model on the honeycomb lattice, clarifying discrepancies with previous studies.

Findings

Consistent ν = 0.691(2) using finite-size scaling with correction

Large N data yields ν = 0.707(6), aligning with Monte Carlo results

Highlights the subtlety in determining critical exponents from finite-size data

Abstract

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent $\nu$ are analyzed in great detail. Remarkly, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent $\nu = 0.691(2)$ with that calculated in \cite{Wenzel08}. However by using the data with large number of spins $N$, we obtain $\nu = 0.707(6)$ which agrees with the most accurate Monte Carlo O(3) value $\nu = 0.7112(5)$ as well.