We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.

中文翻译：

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离散时空中的各向异性 Landau-Lifshitz 模型

我们构建了离散时空中经典相互作用自旋的可积晶格模型，代表具有单轴各向异性的晶格 Landau-Lifshitz 铁磁体的离散时间模拟。作为一个应用，我们使用这种显式离散辛积分方案来计算作为各向异性和化学势函数的自旋德鲁德权重和扩散常数。我们在非磁化扇区中的易轴和易平面状态中展示了定性不同的行为。在接近各向同性点时，我们还发现了扩散常数的代数发散，表明自旋超扩散的交叉。