Abstract This work presents a comprehensive analysis of key elements determining the efficiency of Simulated Tempering implementations for lattice models. Important aspects like the proper choice of the replicas temperature set ϒ R , their quantity R and adequate estimation of the weight factors (establishing the probabilities of jumps between the replicas) are considered. A number of tests to validate distinct ST implementations – as well as to characterize convergence and fluctuations (this latter, after reaching the steady condition) of the thermodynamic estimators – is proposed. Also, by combining the ST method with the so called fixed exchange frequency protocol (to determine ϒ R ), a new procedure to calculate critical temperatures is developed. As cases studies, two commonly addressed lattice models are discussed, the Blume–Emery–Griffiths and Bell–Lavis. Their detailed investigation at the coexistence condition or under first order phase transition regimes allows to properly inspect factors like, pace of convergence, tunneling between replicas and minimal values of the highest replica temperature T R , affecting a good overall performance of the ST method.

中文翻译：

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分析和验证相变状态下的模拟回火实施

摘要 这项工作对决定晶格模型模拟回火实现效率的关键要素进行了全面分析。重要的方面，如副本温度集 ϒ R 的正确选择、它们的数量 R 和权重因子的适当估计（建立副本之间跳跃的概率）被考虑在内。提出了许多测试来验证不同的 ST 实现——以及表征热力学估计器的收敛和波动（后者，在达到稳定条件后）。此外，通过将 ST 方法与所谓的固定交换频率协议（以确定 ϒ R ）相结合，开发了一种计算临界温度的新程序。作为案例研究，讨论了两种常见的晶格模型，Blume-Emery-Griffiths 和 Bell-Lavis。他们在共存条件下或在一阶相变状态下的详细研究允许正确检查诸如收敛速度、复制品之间的隧道和最高复制品温度 TR 的最小值等因素，从而影响 ST 方法的良好整体性能。