General properties of classical tensor network methods in the thermodynamic limit

Studying emergent phenomena in classical statistical physics is known to be one of the most computationally difficult problems. One method to study these problems is with tensor networks, which renormalize the systems for the most relevant states ranked by entropy. In contrast with Monte Carlo sampling, tensor algorithms avoid any statistical errors from sampling and can compute billions of spins. An explosion of numerical algorithms which compute general properties of a statistical physics system such as specific heat, magnetization, and free energies are available. However, an overview of which tensor algorithms are best and where they must be improved would be highly advantageous for the scientific community and help with new modeling and discoveries. In this talk, we compare and contrast the algorithms found in literature, make recommendations of which algorithms to use, and speculate on improvements in future algorithms. We additionally present a unified coding framework within the DMRjulia library.