The two-particle-irreducible vertex of the two-dimensional lattice model across the Ising transition
This paper reconstructs the two-particle-irreducible vertex of the two-dimensional lattice model across the Ising transition using Monte Carlo data, revealing a multidimensional soft sector dominated by ferromagnetic and nematic channels, and demonstrates that approximating the fully irreducible vertex as a local contact term accurately reproduces self-energy dynamics via parquet and Schwinger-Dyson equations, thereby providing a first-principles benchmark for the dynamical local-vertex approximation (DA).