Neural network evidence of a weakly first-order phase transition for the two-dimensional 5-state Potts model

A universal (supervised) neural network (NN), which is trained only once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using two artificially made configurations as the training set. Due to the unique features of the employed NN, results associated with systems consisting of over 4,000,000 spins can be obtained with ease, and convincing NN evidence showing that the investigated phase transition is weakly first order is reached.