Arbitrarily Weak First Order Phase Transitions in the 3D Standard Ashkin-Teller Model by MC Computer Experiments

The first order phase transition line in the vicinity of the tricritical Ising point region is studied in the 3D standard Ashkin-Teller model on a cubic lattice. The large-scale Monte Carlo computer experiments using the Binder- and Challa-like cumulants, the latter modified by Musial, are proposed and performed. Specific behavior of the Challa-Musial cumulants for weak first order phase transitions is discovered and its interpretation is proposed. The paper proves the arbitrarily weak first order character of phase transitions when approaching to the Ising point.