2010/10/29 by F. -J. Jiang, Jiang, F. -J.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #hep-lat #hep-ph
paper · pdf · doi:10.48550/arxiv.1010.6267
7 pages, 11 figures, 1 table, longer version of arXiv:0911.0653. The validity of the unconventional finite-size scaling proposed in arXiv:0911.0653 is verified
arxiv created 2010/10/29 · arxiv updated 2010/11/01
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 \citeWenzel08, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of ρs1 L and ρs2 L, where L stands for the spatial box size used in the simulations and ρsi with i ∈ \1,2\ is the spin-stiffness in i-direction. From our Monte Carlo data, we find that ρs2 L suffers a much less severe correction compared to that of ρs1 L. Therefore ρs2 L is a better quantity than ρs1 L for finite-size scaling analysis concerning the limitation of the availability of large volumes data in our study. Further, motivated by the so-called cubical regime in magnon chiral perturbation theory, we additionally perform a finite-size scaling analysis on our Monte Carlo data with the assumption that the ratio of spatial winding numbers squared is fixed through all simulations. As a result, the physical shape of the system remains fixed in our calculations. The validity of this new idea is confirmed by studying the phase transition driven by spatial anisotropy for the ladder anisotropic Heisenberg model. With this new strategy, even from ρs1 L which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent ν which is consistent with the expected O(3) value by using only up to L = 64 data points.