Nematic phase in the J₁-J₂ square lattice Ising model in an external field

The J$_1$-J$_2$ Ising model in the square lattice is a minimal model with competing nearest-neighbor and next-nearest-neighbor interactions. Its phase diagram in the temperature versus $\kappa=J_2/|J_1|$ plane has three phases: ferromagnetic and a striped phase at low T and a disordered phase at high T. The nature of this phase diagram has been debated in the last 20 years. Instead, the effects of an external field on the phase diagram have been much less studied. We have studied it by two
approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square
approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an
Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and
disordered phases.
Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence
of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for
selected values of the parameter $\kappa$ which measures the relative strength of the competing
interactions. From the CVM in the square approximation we obtain a line of second order transitions between
the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order.
The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with
the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach
definite conclusions about the nature of the transitions.