三维XY模型中的构象温度
Configurational Temperature in the 3D XY Model
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中文总结 AI 辅助
本研究以三维含虚化学势XY模型为对象，利用8³格点模拟验证构象温度估计量，发现其在对称相吻合预期、有序相偏差源于有限尺寸与离散化误差，该工具可用于格点场论模拟的算法正确性与热化评估。
中文摘要 AI 辅助
我们研究构象温度估计量作为三维XY模型（含虚化学势）的蒙特卡罗模拟与朗之万模拟的诊断工具。该估计量仅依赖场构象，可为数值采样算法提供严格的内部一致性检验。我们在8³格点上，针对β=0.2-0.7的一系列耦合值，分别采用实朗之万动力学与梅特罗波利斯蒙特卡罗算法开展模拟。我们的作用密度结果与小β下的强耦合展开预测吻合度极高，为两种模拟方法提供了重要验证。测得的构象温度估计量值在对称相内与预期值1吻合良好，但在有序相中出现系统性偏差。我们将这些偏差主要归因于格点体积相对较小带来的有限尺寸效应与离散化误差。我们的结果表明，构象温度估计量是格点场论模拟中评估热化状态与算法正确性的重要诊断工具，这类诊断对实化学势下的研究尤为关键——实化学势下会出现符号问题，常规验证方法可靠性会下降。
英文摘要
We investigate the configurational temperature estimator as a diagnostic tool for Monte Carlo and Langevin simulations of the three-dimensional XY model with an imaginary chemical potential. This estimator depends only on the field configurations. It provides a stringent internal consistency check for numerical sampling algorithms. We perform simulations using both real Langevin dynamics and the Metropolis Monte Carlo algorithm on an $8^3$ lattice across a range of coupling values, $β= 0.2 - 0.7$. Our results for the action density are in excellent agreement with strong-coupling expansion predictions at small $β$, providing an important validation of both simulation approaches. The measured value of the configurational temperature estimator shows good agreement with its expected value of unity in the symmetric phase. However, systematic deviations appear in the ordered phase. We attribute these deviations primarily to finite-size effects and discretization artifacts associated with the relatively small lattice volume. Our results demonstrate that the configurational temperature estimator provides a valuable diagnostic for assessing thermalization and algorithmic correctness in lattice field theory simulations. Such diagnostics are particularly important in preparation for studies at real chemical potential, where sign problems arise and conventional validation methods become less reliable.
