Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model

Abstract

With the help of the improved Monte Carlo renormalization-group scheme, we numerically investigate the renormalization group flow of the antiferromagnetic Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and its effective Hamiltonian, 2N-component chiral ${\varphi }^4$ model which is used in the field-theoretical studies. We find that the XY-STA model with the lattice size $126\times 144\times 126$ exhibits clear first-order behavior. We also find that the renormalization-group flow of STA model is well reproduced by the chiral ${\varphi }^4$ model, and that there are no chiral fixed point of renormalization-group flow for N=2 and 3 cases. This result indicates that the Heisenberg-STA model also undergoes first-order transition.

v1:15 pages, 15 figures v2:updated references v3:added comments on the higher order irrelevant scaling variables v4:added results of larger sizes v5:final version to appear in J.Phys.Soc.Jpn Vol.72, No.1

References in corpus (1)

• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle

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