三维有质量重整化群微扰展开的分析：一个微妙的例子
Analysis of the 3d massive renormalization group perturbative expansions: a delicate case
摘要：
本文分析了定维空间微扰重整化群方法在临界现象理论中的有效性。三种模型被认为是：O（N）模型，立方模型和反铁磁模型定义在堆叠的三角晶格。我们认为所有的模型在固定的d=3和分析目前用于计算临界指数的再确认程序。我们首先证明了，对于O（N）模型，重算并不能消除所有的非物理（虚假）不动点（FP）。然后仔细研究了伪频和Wilson-Fisher FP对重构参数的依赖性。在威尔逊-费舍尔FP的临界指数显示出弱的依赖性的再结晶参数。相反，伪FP处的指数以及伪FP的存在强烈依赖于这些参数。对于三次模型，发现了一个新的稳定FP，其性质也强烈依赖于恢复参数。这似乎是假的，正如预期的那样。至于受挫模型，根据自旋分量数量的值，有两种情况。当N大于临界值Nc时，稳定FP与Wilson-Fisher FP具有共同的特征。相反，当N<Nc时，在稳定FP处得到的结果与在O（N）和立方模型的伪FP处得到的结果相似。我们的结论是，从这个分析，稳定FP发现N3<Nc in frustrated models is spurious. Since Nc>，我们得出结论，XY和海森堡阻挫磁铁的转变是一级。
英文摘要：
The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d=3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N<Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N) and cubic models. We conclude from this analysis that the stable FP found for N<Nc in frustrated models is spurious. Since Nc>3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
