Monte Carlo study on Heisenberg model with local dipolar interaction

Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative 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 $\lambda$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $\lambda =\mathrm{\infty }$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $\lambda =8$ (e.g. $\nu =0.601(2){(}_{-2}^{+0})$ in the local Heisenberg-dipolar model while $\nu =0.712(1){(}_{-0}^{+3})$ in the Heisenberg model), and the spin correlation function has a feature that it becomes divergence-free, implying the lack of conformal invariance.