A new method for conservative dynamics in contact with a thermal bath: study of the classical Heisenberg antiferromagnet

To simulate spin systems in the canonical ensemble it is common to use Montecarlo [1]. However, Montecarlo dynamics is far from the physical one, especially when symmetries and conservation laws change the dynamic critical exponents, as in the important case of antiferromagnets. For this reason, the use of the more physical spin dynamics has become a standard in the field [2].

Yet, within micro-canonical spin dynamics it is not obvious how to add thermal fluctuations that conserve the magnetization, so that thermalization is ensured by evolving initial conditions drawn with the canonical distribution. Although progress has been done by combining Kawasaki canonical Montecarlo with microcanonical spin-dynamics [3], it would be highly convenient to have a simple spin dynamics coupled to a heat bath that respects the conservation law.

Here we introduce such an algorithm and we test it on the Heisenberg antiferromagnet in d=3. We show that at Tc the algorithm reproduces the right value of the dynamical critical exponent, z=1.5, while in the low temperature phase spin waves correctly emerge. The kinetic coefficient of the conservative heat bath is connected in a simple way to the microscopic parameters of the spin-phonon coupling, thus explaining softening of the spin-wave peaks.

[1] K. Chen, A.M. Ferrenberg and D. P. Landau, PHYSICAL REVIEW B 48, 3249 (1993)

[2] D P Landau and M Krech 1999 J. Phys.: Condens. Matter 11 R179

[3] R. Nandi and U. C. Täuber, PHYSICAL REVIEW B 99, 064417 (2019).