论文标题
在概率空间中的定向步行，可以找到旋转模型的平均现场解决方案
A directed walk in probability space that locates mean field solutions to spin models
论文作者
论文摘要
尽管它们的正式简单性，但大多数晶格旋转模型即使在平均野外理论的简化假设下也很容易解决。在此手稿中，我们提出了一种为经典连续自旋生成平均场解决方案的方法。我们将注意力集中在具有非本地相互作用和非周期性边界的系统上，这些系统需要仔细处理现有方法，例如蒙特卡洛采样。我们的方法利用功能优化来得出封闭形式的最佳条件，并到达自一致的平均场方程。我们表明，这种方法在收敛速度和准确性方面显着优于常规的蒙特卡洛采样。为了传达该方法背后的一般概念，我们首先证明了它在简单系统中的应用 - 外部电场中的有限的一维偶极链。然后，我们描述该方法如何自然地扩展到更复杂的自旋系统和连续的场理论。此外，我们通过在各种维度的非周期性旋转模型上强调其实用性来说明方法的功效。
Despite their formal simplicity, most lattice spin models cannot be easily solved, even under the simplifying assumptions of mean field theory. In this manuscript, we present a method for generating mean field solutions to classical continuous spins. We focus our attention on systems with non-local interactions and non-periodic boundaries, which require careful handling with existing approaches, such as Monte Carlo sampling. Our approach utilizes functional optimization to derive a closed-form optimality condition and arrive at self-consistent mean field equations. We show that this approach significantly outperforms conventional Monte Carlo sampling in convergence speed and accuracy. To convey the general concept behind the approach, we first demonstrate its application to a simple system - a finite one-dimensional dipolar chain in an external electric field. We then describe how the approach naturally extends to more complicated spin systems and to continuum field theories. Furthermore, we numerically illustrate the efficacy of our approach by highlighting its utility on nonperiodic spin models of various dimensionality.
