Lattice models from mathematical physics often lead to high-dimensional integration problems that need to be solved numerically. Conventional algorithms are prone to the critical slowing down, which refers to extremely slow convergence rates or even a lack of convergence of numerical algorithms near phase transitions or towards the continuum limit. The goal of this project is to investigate mathematically whether tensor lattice methods, which have recently shown promising computational results in the physics and chemistry communities, can indeed mitigate the critical slowing down.