论文标题
随机场ISING模型和巴黎 - 苏拉斯超对称性。第二部分。重新归一化组
Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
论文作者
论文摘要
我们在上临界尺寸6附近的复制Landau-Ginzburg的描述中重新扰动RG分析。在野外工作，与弱耦合的Parisi-Sourlas Supersmpers-Mepersmpermmememmememmemempric固定点（Cardy，1985年）相互作用（我们寻找可以消除SUSY RG流动的相互作用）的相互作用。这个问题减少了研究“领导者”的异常维度 - $ s_n $ invariant扰动的最低尺寸零件。根据他们的对称性，领导者的运营商被归类为无人可乐，susy-worlable或susy-null。 Susy可辩护的领导者还被归类为属于$ \ textrm {osp}（d | 2）$表示的超级多个多重组。我们列举所有领导者最多6D维度$δ= 12 $，并计算其扰动异常维度（最多两个循环）。因此，我们确定了两个扰动（与Susy-Null和不舒服的领导者）相关，低于关键维度$ D_C \约4.2 $ - $ 4.7 $。这支持了Susy固定点的所有$ 3 <d \ leq 6 $的情况，但对于$ d <d_c $而变得不稳定。
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 $d < d_c$.
