论文标题
虚弱的伊辛模型的批判行为：六循环$ \ sqrt \ varepsilon $扩展研究
Critical behavior of weakly disordered Ising model: Six-loop $\sqrt \varepsilon$ expansion study
论文作者
论文摘要
三维弱稀释的淬灭ISING模型的临界行为是在最小$ 4-ε$空间尺寸的最小减法方案中获得的六环重新归一化组扩展的基础的。为此，在复制限制$ n \ rightarrow 0 $中分析了带有立方对称性的$ ϕ^4 $字段理论。与重新归一化的群体扩展以及重新归一化的耦合一起扩展，提出了关键指数的$ \ sqrt {\ varepsilon} $扩展。通过在$ \ sqrt {\ varepsilon} $系列和初始的恢复归化组扩展上，通过不同的重新召集过程获得了物理三维系统的相应数值估计。后一种方法给出的结果与他们在蒙特卡洛模拟中获得的对应者达成了很好的协议，同时重新庆祝$ \ sqrt {\ varepsilon} $系列本身本身令人失望。
The critical behavior of three-dimensional weakly diluted quenched Ising model is examined on the base of six-loop renormalization group expansions obtained within the minimal subtraction scheme in $4-ε$ space dimensions. For this purpose the $ϕ^4$ field theory with cubic symmetry was analyzed in the replica limit $n\rightarrow 0$. Along with renormalization group expansions in terms of renormalized couplings the $\sqrt{\varepsilon}$ expansions of critical exponents are presented. Corresponding numerical estimates for the physical, three-dimensional system are obtained by means of different resummation procedures applied both to the $\sqrt{\varepsilon}$ series and to initial renormalization group expansions. The results given by the latter approach are in a good agreement with their counterparts obtained experimentally and within the Monte Carlo simulations, while resumming of $\sqrt{\varepsilon}$ series themselves turned out to be disappointing.
