Monte Carlo study of the Heisenberg model with local dipolar interaction

Aharony and Fisher showed that nonlocal dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point called the dipolar fixed point. The nonperturbative nature of the new fixed point, however, has not been uncovered for many decades. Inspired by the recent understanding that the dipolar fixed point is scale invariant but not conformal invariant, we perform the Monte Carlo simulation of the local Heisenberg-dipolar model on the lattice of ${40}^{3}$ by introducing the local cost function parameterized by a parameter $\ensuremath{\lambda}$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $\ensuremath{\lambda}=\ensuremath{\infty}$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $\ensuremath{\lambda}=8$ [e.g., $\ensuremath{\nu}=0.601(2){(}_{\ensuremath{-}2}^{+0}){{(}_{\ensuremath{-}4}^{+5})}_{{\ensuremath{\beta}}_{c}}$ in the local Heisenberg-dipolar model while $\ensuremath{\nu}=0.712(1){(}_{\ensuremath{-}0}^{+3}){{(}_{\ensuremath{-}1}^{+1})}_{{\ensuremath{\beta}}_{c}}$ in the Heisenberg model], and the spin correlation function has a feature that it becomes divergence free, implying the lack of conformal invariance.