Phase transitions in a frustrated Ising antiferromagnet on a square lattice

Abstract

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- (J1<0) and second-nearest-neighbor (J2<0) interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of R=J2/|J1|. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to R=-0.5 not only between the superantiferromagnetic and paramagnetic (R<-0.5) but also between antiferromagnetic and paramagnetic (R>-0.5) phases.

Quantum Ising model on the frustrated square lattice

“…It is worth to stress that the nature of the phase transitions in this model is a topic of current debate. For instance, an effective field-theory study using clusters of up to 9 sites indicated the presence of a discontinuous phase transition between PM and AF states [23]. However, our results indicating only continuous phase transitions for the PM/AF phase boundary are in agreement with Monte Carlo simulations [10] and cluster variation method calculations [9].…”

“…In particular, our approach indicates that tricriticality occurs at g * = 0.66 [5,6], which is much closer to the Monte Carlo simulations (g * MC ≈ 0.67) [12,13] than the effective field theory predictions (g * EFT = 0.97) for the largest cluster considered in Ref. [23]. It reinforces that the present approach incorporates important geometrical features of the model, providing an appropriate starting point to study the role of transverse field.…”

“…It indicates that the nature of the phase transitions is correctly incorporated within a four-site approximation, allowing to explore transverse field effects without appealing to the exact diagonalization of larger matrices, which would become computationally expensive taking into account the self-consistent procedure. In addition, intermediary cluster sizes (4 < n s < 16) can imply in clusters that are incompatible with the SAF state [6,23]. Therefore, in the present work we adopt the four-site CMF approach, which is described in the following.…”

Tricritical behaviour of the frustrated Ising antiferromagnet on the honeycomb lattice

“…Since only an approximate expression exists for the free energy at finite temperature in the frame of the EFT based on any spin cluster (see, e.g. [12,19]), we have confined our calculations only to the second-order phase transitions, including the TCP.…”

Various Charge-Ordered States in the Extended Hubbard Model with On-Site Attraction in the Zero-Bandwidth Limit

“…In particular, the MCS predicts that FCO phase does not exist at any T > 0 [34]. Moreover, forμ = 0 and the SQ lattice the first-order CBO-SCO transition is not present at T > 0 and these two phases are separated by the NO phase region [34,40,41]. The situation changes in three dimensions for simple cubic lattice, where that transition occurs [42].…”