We present a modification of the Rose-Machta algorithm (Phys. Rev. E 100
(2019) 063304) and estimate the density of states for a two-dimensional
Blume-Capel model, simulating $10^5$ replicas in parallel for each set of
parameters. We perform a finite-size analysis of the specific heat and Binder
cumulant, determine the critical temperature along the critical line, and
evaluate the critical exponents. The results obtained are in good agreement
with those obtained previously using various methods -- Markov Chain Monte
Carlo simulation, Wang-Landau simulation, transfer matrix, and series
expansion. The simulation results clearly illustrate the typical behavior of
specific heat along the critical lines and through the tricritical point.

我们使用 Rose-Machta 算法的改进方法，估算了二维 Blume-Capel 模型的态密度，通过对参数集合进行每个集合进行 $10^5$ 个副本的并行模拟。我们对比特定热容和 Binder 累积量进行有限大小分析，确定了临界温度、评估了临界指数。结果与之前使用各种方法获得的结果（马尔可夫链蒙特卡洛模拟、Wang-Landau 模拟、传递矩阵和级数展开）非常吻合。模拟结果清楚地揭示了特定热容在临界线和三重临界点附近的典型行为。

微正则模型分析与微正则种群退火方法

Blume-Capel model analysis with microcanonical population annealing  method

As powerful as machine learning (ML) techniques are in solving problems
involving data with large dimensionality, explaining the results from the
fitted parameters remains a challenging task of utmost importance, especially
in physics applications. Here it is shown how this can be accomplished for the
ferromagnetic Ising model, the target of many ML studies in the last years. By
using a neural network (NN) without any hidden layers and the symmetry of the
Hamiltonian to find the critical temperature for the continuous phase
transition of the model, an explanation of its strategy is found. This allows
the prediction of the minimal extension of the NN to solve the problem when the
symmetry is not known, which is also explainable.

使用神经网络和哈密顿的对称性来解释和预测具有大数据维度的物理应用中的铁磁伊辛模型的临界温度。

解释 Ising 模型的机器学习解决方案

Explaining the Machine Learning Solution of the Ising Model

Superconductors have been among the most fascinating substances, as the
fundamental concept of superconductivity as well as the correlation of critical
temperature and superconductive materials have been the focus of extensive
investigation since their discovery. However, superconductors at normal
temperatures have yet to be identified. Additionally, there are still many
unknown factors and gaps of understanding regarding this unique phenomenon,
particularly the connection between superconductivity and the fundamental
criteria to estimate the critical temperature. To bridge the gap, numerous
machine learning techniques have been established to estimate critical
temperatures as it is extremely challenging to determine. Furthermore, the need
for a sophisticated and feasible method for determining the temperature range
that goes beyond the scope of the standard empirical formula appears to be
strongly emphasized by various machine-learning approaches. This paper uses a
stacking machine learning approach to train itself on the complex
characteristics of superconductive materials in order to accurately predict
critical temperatures. In comparison to other previous accessible research
investigations, this model demonstrated a promising performance with an RMSE of
9.68 and an R2 score of 0.922. The findings presented here could be a viable
technique to shed new insight on the efficient implementation of the stacking
ensemble method with hyperparameter optimization (HPO).

利用堆叠机器学习方法对超导材料的复杂特性进行训练，以准确预测临界温度。与先前的研究相比，该模型表现出有希望的性能，RMSE 为 9.68，R2 得分为 0.922。本研究的结果可为堆叠集成方法与超参数优化的高效实现提供新的见解。

机器学习估计超导体临界温度的方法调查

Investigation on Machine Learning Based Approaches for Estimating the  Critical Temperature of Superconductors

We estimate a statistical model to predict the superconducting critical
temperature based on the features extracted from the superconductor's chemical
formula. The statistical model gives reasonable out-of-sample predictions: $\pm
9.5$ K based on root-mean-squared-error. Features extracted based on thermal
conductivity, atomic radius, valence, electron affinity, and atomic mass
contribute the most to the model's predictive accuracy. It is crucial to note
that our model does not predict whether a material is a superconductor or not,
it only gives predictions for superconductors.

本文通过提取超导体化学式的特征来预测其超导临界温度，其中热导率、原子半径、价态、电子亲和力和原子质量是预测精度最高的贡献因素。需要注意的是，该模型仅针对超导体进行预测。