Mangetic phase transition for three-dimensional Heisenberg weak random anisotropy model: Monte Carlo study

TL;DR

This study uses Monte Carlo simulations to investigate the magnetic phase transition to a quasi-long-range order phase in a three-dimensional Heisenberg model with weak random anisotropy, confirming theoretical predictions of a second-order transition.

Contribution

It provides numerical evidence for a second-order magnetic phase transition to QLRO in a 3D Heisenberg model with weak random anisotropy, supporting recent theoretical predictions.

Findings

Critical coupling for isotropic RA axes: 0.70435(2)

Critical coupling for cubic RA axes: 0.70998(4)

Same critical exponent 1/nu = 1.40824(0) for both cases

Abstract

Magnetic phase transition (MPT) to magnetic quasi-long-range order (QLRO) phase in a three-dimensional Heisenberg weak (D/J=4) random anisotropy (RA) model is investigated by Monte Carlo simulation. The isotropic and cubic distributions of RA axes are considered for simple-cubic-lattice systems. Finite-size scaling analysis shows that the critical couplings for the former and latter are K_c= 0.70435(2) and K_c=0.70998(4), respectively. While the critical exponent 1/\nu =1.40824(0) is the same for both cases. A second-order MPT to the QLRO phase is therefore evidenced to be possible in favor with the existence of the QLRO predicted by recent functional renormalization group theories.