论文标题
Landau-Potts现场理论中的跨界指数，分形维度和对数
Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
论文作者
论文摘要
We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_q$ in $d=6-ε$ (Landau-Potts field theories) and $d=4-ε$ (hypertetrahedral models) up to three loops.We use our results to determine the $ε$-expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and森林（$ q \ to0 $）和债券渗透（$ q \ to1 $）。我们还明确验证了相关操作员在分析持续时的自然值$ q $的几个预期退化性，它们与CFT相关器的对数校正有关，并使用$ε$ - 扩展来确定此类对数的通用系数。
We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_q$ in $d=6-ε$ (Landau-Potts field theories) and $d=4-ε$ (hypertetrahedral models) up to three loops.We use our results to determine the $ε$-expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ($q\to0$), and bond percolations ($q\to1$). We also explicitly verify several expected degeneracies in the spectrum of relevant operators for natural values of $q$ upon analytic continuation, which are linked to logarithmic corrections of CFT correlators, and use the $ε$-expansion to determine the universal coefficients of such logarithms.
