We studied a layered metamagnetic Ising model with competing ferromagnetic and antiferromagnetic interactions on a square lattice. The model is formed of ferromagnetic chains coupled by an antiferromagnetic interaction. Using Monte Carlo simulations we have determined the phase diagram of the model, which exhibits a tricritical point. By exploring the short-time scaling dynamics, we have found the dynamic and static critical exponents along the continuous transition line between the antiferromagnetic and paramagnetic phases.
In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width
n (hn) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants $\ensuremath{\delta}$. The obtained results indicate that the
h1-TL phase transition line is continuous up to $\ensuremath{\delta}=1.2585$, while for the
h2-TL line a weak first-order character is found in the interval $1.2585\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.36$ and becomes continuous for $1.37\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.9$. This result suggests the existence of a tricritical point close to $\ensuremath{\delta}=1.37$. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on $\ensuremath{\delta}$ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the ${h}_{1}\ensuremath{-}{h}_{2}$ line, i.e., at $\ensuremath{\delta}=1.2585$, the critical phase corresponding to the ${h}_{1}\ensuremath{-}\mathrm{TL}$ transition coexists with the
h2 phase.