Wang-Landau simulations of the coupled magnetic and nematic transitions in disordered iron-based superconductors

In many iron-based superconductors, nematicity and magnetism are found to be closely related and occurring at comparable temperatures. While many works have discussed the character of these coupled transitions in clean systems, the impact of disorder, like random strain, has not been elucidated. Here we perform Monte Carlo simulations of an appealing model that captures these two transitions, namely, the 2D anisotropic Ising-O(3) model. For sufficiently large anisotropy in the exchange coupling, there is a direct first-order transition from the paramagnetic tetragonal phase to the low-temperature phase that displays both spin and nematic (Ising) orders. This transition splits into two separate transitions as the anisotropy decreases, giving rise to a nematic intermediate phase. We study both clean and disordered systems and compare conventional algorithms, such as Metropolis and Wolff, to an implementation using the Wang-Landau algorithm. The latter avoids the supercritical slowing down associated with the first-order transitions, providing an efficient way to probe the complicated free energy landscapes near the multi-critical point. Phase diagrams are obtained and compared to experimental results.