Nematic phase in the J$_1$-J$_2$ square lattice Ising model in an external field

TL;DR

This study identifies a new Ising-nematic phase in the J$_1$-J$_2$ square lattice model under an external field, using CVM and Monte Carlo methods, revealing complex phase transitions and a novel intermediate phase.

Contribution

The paper reports the discovery of an Ising-nematic phase in the J$_1$-J$_2$ model, not previously documented, using a combination of CVM and Monte Carlo simulations.

Findings

Identification of a new Ising-nematic phase between stripe and disordered phases.

Qualitative agreement between CVM and Monte Carlo results supports the nematic phase.

Phase diagrams showing second and first order transitions in temperature-field space.

Abstract

The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied 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. Suitable order parameters are defined and the phase diagram of the model is obtained. 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 $\kappa=J_2/|J_1|$ 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.