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arXiv:2008.11541 · Physical review. E

Critical dynamics of anisotropic antiferromagnets in an external field

Riya Nandi, Uwe Claus Täuber

Published Nov 11, 2020• 7 citations
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Abstract

We numerically investigate the nonequilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The nonconserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and the conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.

DOI
10.1103/physreve.102.052114

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We numerically investigate the nonequilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The nonconserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and the conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.
We numerically investigate the stationary and nonequilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the nonconserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin-exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization-group prediction: While the critical aging collapse exponent assumes a universal value, the associated temporal decay exponent in the two-time spin autocorrelation function depends on the initial distribution of the conserved fields; here, specifically on the width of the initial spin orientation distribution.
We investigate the relaxation dynamics of two distinct non-equilibrium processes: relaxation of three-dimensional antiferromagnetic lattice spin models with Heisenberg interaction following a critical quench, and a one-dimensional exclusion process inspired by the gear-like motion of molecular motors. In a system of three-dimensional Heisenberg antiferromagnets the non-conserved staggered magnetization components couple non-trivially to the conserved magnetization densities inducing fully reversible terms that enter the Langevin dynamic equation. We simulate the exact microscopic dynamics of such a system of antiferromagnets by employing a hybrid simulation algorithm that combines the reversible spin precession implemented by the fourth-order Runge-Kutta integration method with the standard relaxational dynamics at finite temperatures using Monte Carlo updates. We characterize the dynamic universality class of this system by probing the early temporal window where the system exhibits aging scaling properties. We also verify an earlier renormalization group prediction that the temporal decay exponent in the two-time spin autocorrelation function exhibits non-universality, specifically it depends on the width of the initial spin orientation distribution. We employ a similar numerical technique to study the critical dynamics of an anisotropic Heisenberg antiferromagnet in the presence of an external field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. We study the aging scaling dynamics for the model C critical line, probe the model F critical line by investigating the system size dependence of the characteristic spin-wave frequencies near criticality, and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point. We introduce a one-dimensional non-equilibrium lattice gas model representing the processive motion of dynein molecular motors over the microtubule. We study both dynamical and stationary state properties for the model consisting of hardcore particles hopping on the lattice with variable step sizes. We find that the stationary state gap-distribution exhibits striking peaks around gap sizes that are multiples of the maximum step size, for both open and periodic boundary conditions, and verify this using a mean-field calculation. For open boundary conditions, we observe intriguing damped oscillator-like distribution of particles over the lattice with a periodicity equal to the maximum step size. To characterize transient dynamics, we measure the mean square displacement that shows weak superdiffusive growth with exponent γ≈ 1.34 for periodic boundary and ballistic growth ( γ≈ 2) for open boundary conditions at early times. We also study the effect of Langmuir dynamics on the density profile.
A complete two-loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in three-dimensional anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached.
We study the critical dynamics of stochastic models appropriate for describing bicritical and tetracritical points in anisotropic antiferromagnetic systems. The dynamic exponents and the transient exponents are calculated by renormalized field theory up to two-loop order. In the presence of reversible mode-coupling terms, two-loop contributions establish bicritical dynamic scaling in the restricted sense and invalidate recent predictions based on mode-coupling arguments. In the case of an n-component relaxational model total dynamic scaling is found to O (ε2) both at the bicritical (n≲3) and the tetracritical (4≲n<11) points.
The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilities and the probability distribution of the magnetization to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.
With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional antiferromagnetic Ising model with a globally conserved magnetization m(s) (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the autocorrelation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of m(s)=0 is the same as that without a conserved quantity, but the universality class of nonzero m(s) is different.