Field theory conjecture for loop-erased random walks

Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $ϕ^4$ theory with $n\to -2$ and loop-erased random walks

Driven periodic elastic systems such as charge-density waves (CDWs) pinned by impurities show a non-trivial, glassy dynamical critical behavior. Their proper theoretical description requires the functional renormalization group. We show that their critical behavior close to the depinning transition is related to a much simpler model, $O(n)$-symmetric $ϕ^4$ theory in the unusual limit of $n\to -2$. We demonstrate that both theories yield identical results to 4-loop order and give both a perturbative and a non-perturbative proof of their equivalence. As we show, both theories can be used to desc…

二维无无序的分数扩散

Fractional diffusion without disorder in two dimensions

研究二维中简单局部约束使缺陷呈现可调亚扩散，通过冰型和二聚体型模型揭示丰富动力学现象及有效分数扩散方程，缺陷路径分形维数为5/4，该研究对人工自旋冰和量子模拟器等平台有重要意义。