铁磁球模型的非对称Langevin动力学
Asymmetric Langevin dynamics for the ferromagnetic spherical model
摘要：
本工作致力于研究空间不对称性和不可逆性对自旋系统动力学性质的影响。考虑具有非对称线性Langevin动力学的铁磁球模型。这种不对称动力学是不可逆的，即，破坏了细致平衡，因为违反了作用和反作用的原则。因此，涨落耗散定理不再成立。然而，定态仍然是吉布斯的，即，配置的权重由对应于铁磁哈密顿量的玻尔兹曼因子给出。该模型在任何维度上都是完全可解的，从而可以对随时间变化的观测量进行分析评估。我们证明了存在两个制度的违反波动耗散定理的非平衡定态：一个制度的弱违反的固定波动耗散比是有限的，但小于统一和不断变化的不对称性，和一个制度的强违反的波动耗散比渐近消失。这种现象首先在不对称动力学伊辛链中被发现。这些结果表明，这种新的非平衡定态动力学跃迁可能是相当普遍的。我们还进行了系统的分析几个政权的利益，无论是静态或瞬态，在不同的维度和不同阶段的模型。
英文摘要：
The present work pursues the investigation of the role of spatial asymmetry and irreversibility on the dynamical properties of spin systems. We consider the ferromagnetic spherical model with asymmetric linear Langevin dynamics. Such an asymmetric dynamics is irreversible, i.e., breaks detailed balance, because the principle of action and reaction is violated. The fluctuation-dissipation theorem therefore no longer holds. The stationary state is however still Gibbsian, i.e., the weights of configurations are given by the Boltzmann factor corresponding to the ferromagnetic Hamiltonian. The model is exactly solvable in any dimension, enabling an analytical evaluation of time-dependent observables. We show the existence of two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite but less than unity and varies continuously with the asymmetry, and a regime of strong violation where the fluctuation-dissipation ratio vanishes asymptotically. This phenomenon was first uncovered in the asymmetric kinetic Ising chain. The present results suggest that this novel kind of dynamical transition in nonequilibrium stationary states might be quite general. We also perform a systematic analysis of several regimes of interest, either stationary or transient, in various dimensions and in the different phases of the model.
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