Baxter–Wu model with fixed magnetization

We study Baxter–Wu triangular model with fixed magnetization in the framework of canonical and microcanonical ensemble, constructing the density of states by Wang–Landau algorithm. We use an approximation similar to a recently developed scheme (critical minimum energy subspace). In this scheme the sampling is not extended to the whole energy spectrum for the given magnetization but it is restricted in a properly determined part of it. We have studied lattices with linear size up to L=840. Our conclusions corroborate analogous conclusions for the square Ising model: An unconventional temperature-driven first-order phase transition take place for lattice sizes above some threshold but this transition ceases to exist at the thermodynamic limit.