随机场伊辛模型与Parisi-Sourlas超对称性部件II。重整化群
Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
摘要：
我们重新审视微扰RG分析在复制的朗道-金斯堡描述的随机场伊辛模型附近的上临界尺寸6。在弱耦合的Parisi-Sourlas超对称不动点（Cardy，1985）附近的场基础上，我们寻找可能破坏超对称RG流稳定并导致降维损失的相互作用。这个问题归结为研究Cardy基中$S_n$不变扰动的最低维部分--“领导者”的反常维数。Leader算子根据其对称性分为不可写、可写和空三种。Susy-可写的领导者被另外分类为属于超原色多重态变换在特定的$\textrm{OSp}(d | 2)$表示。我们列举了所有的领导人到6d维$Δ= 12$，并计算他们的扰动异常尺寸（两个循环）。因此，我们确定两个扰动（与susy空和非susy可写的领导人）成为相关的关键尺寸以下$d_c \approx 4.2$ - $4.7$。这支持对于所有$3 < d \leq 6$都存在SUSY固定点，但对于$d < d_c$变得不稳定的情况。
英文摘要：
We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead to the loss of dimensional reduction. This problem is reduced to studying the anomalous dimensions of "leaders" -- lowest dimension parts of $S_n$-invariant perturbations in the Cardy basis. Leader operators are classified as non-susy-writable, susy-writable or susy-null depending on their symmetry. Susy-writable leaders are additionally classified as belonging to superprimary multiplets transforming in particular $\textrm{OSp}(d | 2)$ representations. We enumerate all leaders up to 6d dimension $Δ= 12$, and compute their perturbative anomalous dimensions (up to two loops). We thus identify two perturbations (with susy-null and non-susy-writable leaders) becoming relevant below a critical dimension $d_c \approx 4.2$ - $4.7$. This supports the scenario that the SUSY fixed point exists for all $3 < d \leq 6$, but becomes unstable for $d < d_c$.
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