标题： 高级关联集团展开 有限温度下的标量场 显示英文标题

标题： Advanced Linked Cluster Expansion. Scalar Fields at Finite Temperature

摘要： 链接簇展开为格点场论的分析和数值研究提供了有用的工具。 展开参数是相互作用强度，相邻格点上的场相互耦合，它们导致自由能、关联函数以及特别是灵敏度的收敛跳跃参数类似级数。 我们考虑在可能在某些方向上有有限扩展的超立方格点上的具有O(N)对称性的标量场，因此包括有限温度T的场论。我们改进已知的并发展新的技术和算法，以增加展开可以计算到的阶数n，从而能够从灵敏度级数中提取关于临界行为的详细信息。 这既涉及简单的矩，也涉及如4点和6点函数这样的高阶相关性，这些用于定义重整化耦合常数。 特别强调有限温度场论。 为了能够测量有限T的临界行为，显式计算的阶数n在格点单位中必须相对于1/T足够大。 2点和4点灵敏度级数计算到了第18阶及更高。 显示英文摘要

摘要： Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they result into convergent hopping parameter like series for free energies, correlation functions and in particular susceptibilities. We consider scalar fields with O(N) symmetric nearest neighbour interactions on hypercubic lattices with possibly finite extension in some directions, thus including field theories at finite temperature T. We improve known and develop new techniques and algorithms to increase the order n the expansions can be computed to in such a way that detailed information on critical behaviour can be extracted from the susceptibility series. This concerns both simple moments as well as higher correlations such as 4- and 6-point functions used to define renormalized coupling constants. Particular emphasis is done on finite temperature field theory. In order to be able to measure finite T critical behaviour, the order of explicit computation n has to be sufficiently large compared to 1/T in lattice units. 2- and 4-point susc. series are computed up to and including the 18th order and beyond.