标题： 低温级数展开的正方格子伊辛模型：基于费舍尔零点的研究 显示英文标题

标题： Low-temperature series expansion of square lattice Ising model: A study based on Fisher zeros

摘要： 低温展开的伊辛模型长期以来一直是凝聚态物理和统计物理领域的重要研究课题。 在本文中，我们给出了在零场和虚场$i(\pi/2)k_BT$情况下，正方形晶格上伊辛分区函数的低温级数中的新结果。 在热力学极限下，自由能低温级数中的系数用费舍尔零点密度函数的显式表达式表示。 当阶数趋于无穷时，系数序列的渐近行为被精确确定，适用于自由能和分区函数的级数。 我们的分析和数值结果表明，该序列的收敛半径取决于具有最小模的费舍尔零点的聚点。 在零场情况下，这个聚点是物理临界点，而在虚场情况下，它对应于非物理奇点。 我们进一步讨论了系数与能量状态简并度之间的关系，使用系数的组合表达式和子图展开。 显示英文摘要

摘要： Low-temperature expansion of Ising model has long been a topic of significant interest in condensed matter and statistical physics. In this paper we present new results of the coefficients in the low-temperature series of the Ising partition function on the square lattice, in the cases of a zero field and of an imaginary field $i(\pi/2)k_BT$. The coefficients in the low-temperature series of the free energy in the thermodynamic limit are represented using the explicit expression of the density function of the Fisher zeros. The asymptotic behaviour of the sequence of the coefficients when the order goes to infinity is determined exactly, for both the series of the free energy and of the partition function. Our analytic and numerical results demonstrate that, the convergence radius of the sequence is dependent on the accumulation points of the Fisher zeros which have the smallest modulus. In the zero field case this accumulation point is the physical critical point, while in the imaginary field case it corresponds to a non-physical singularity. We further discuss the relation between the series coefficients and the energy state degeneracies, using the combinatorial expression of the coefficients and the subgraph expansion.