关于伊辛模型自由能解析域的新结果
New results on the domain of analyticity of the free energy for the Ising model
AI总结：
本研究针对伊辛模型自由能解析性问题，结合多种数学方法推导改进收敛条件，基于维布伦定理的高温扩展得到了更大的解析区域。
AI中文摘要：
我们研究了伊辛模型在非零外磁场、高温及低温条件下自由能的解析性。利用费尔南德斯-普罗卡奇簇展开收敛准则，结合生成函数技术与图论方法，我们在所有三种 regime 中推导出了改进的收敛条件。特别地，生成函数方法在强场与低温 regime 中给出了聚合物和轮廓的更精确估计，而基于维布伦定理的新型高温展开则提供了比文献中经典结果大得多的解析区域。
英文摘要：
We investigate the analyticity of the free energy of the Ising model in the presence of a non-zero external magnetic field, at high temperature, and at low temperature. Using the Fernandez--Procacci convergence criterion for cluster expansions, together with generating-function techniques and graph-theoretical methods, we derive improved convergence conditions in all three regimes. In particular, the generating-function approach yields sharper estimates for polymers and contours in the strong-field and low-temperature regimes, while a new high-temperature expansion based on Veblen's theorem provides a substantially larger analyticity region than the classical results in the literature.
