Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

Abstract

PACS. 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion.Abstract. -We drive a d-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be 'controlled' in a robust manner to target spatially periodic steady states with helical order.How does an imposed steady current of heat or particles alter the dynamics of the isotropic magnet? To answer this question, we extend the equations of motion for the classical O(3) Heisenberg model [1] to include the effects of a uniform current in one spatial direction while retaining isotropy in the order parameter space. The resulting model is a natural generalization of the driven diffusive models of [2] to the case of a 3-component axial-vector order parameter and, as such, is an important step in the exploration of dynamic universality classes [3] far from equilibrium [4]. The form of the local molecular field in which spins precess in this driven state is strikingly different from that at equilibrium [1], and is responsible for all the remarkable phenomena we predict, including a novel nonequilibrium critical point and, in a certain parameter range, a type of turbulence.Here are our results in brief: (i) Despite O(3) invariance in the order-parameter space, the dynamics does not conserve magnetization; (ii) As a temperature-like parameter is lowered, the paramagnetic phase of the model approaches a nonequilibrium critical point in a new dynamic universality class; (iii) Below this critical point, in mean-field theory without stochastic forcing, paramagnetism, ferromagnetism and helical order are all linearly unstable; (iv) Numerical

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“…4. The one-loop correction to Γ 11 2,0 (−q, q) is For each set of solutions, two different 1PI diagrams can be drawn. For V 2 = V 3 = V 4 = 1, the diagrams are given in Fig.…”

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“…(26), to be given by poles in . It is noteworthy that integral (26) has a structure very similar to and has the same logarithmic divergence (by simple power counting) as its equilibrium counterpart [i.e., whenD(q) is replaced by D in Eq.…”

“…It is noteworthy that integral (26) has a structure very similar to and has the same logarithmic divergence (by simple power counting) as its equilibrium counterpart [i.e., whenD(q) is replaced by D in Eq. (26)]. Clearly, the dominant contribution to it comes from p = q 1 + q 2 ∼ 0, which controls the critical behavior of this integral.…”