Tricritical behaviour of the frustrated Ising antiferromagnet on the honeycomb lattice

Abstract

We use the effective-field theory with correlations based on different cluster sizes to investigate phase diagrams of the frustrated Ising antiferromagnet on the honeycomb lattice with isotropic interactions of the strength J 1 < 0 between nearestneighbour pairs and J 2 < 0 between next-nearest neighbour pairs of spins. We present results for the ground-state energy as a function of the frustration parameter R = J 2 /|J 1 |. We find that the cluster-size has a considerable effect on the existence and location of a tricritical point in the phase diagram at which the phase transition changes from the second order to the first one.

The frustrated Ising model on the body-centered cubic lattice

“…However, it is worth to note that the order-disorder phase transitions at g = 2/3 still take place at finite temperature, in agreement with recent findings for the model [1,2]. It means that the effects of frustration on the bcc lattice are weaker when compared to those found for the frustrated square and honeycomb lattices, in which antiferromagnetic second-neighbour interactions can bring the ordering temperature to zero [6,7,[25][26][27][28]. A possible explanation for this reduced sensitivity to frustration can be related to the higher dimensionality of the bcc lattice, which leads to long-range orders that are more robust under thermal fluctuations even when second-neighbour couplings introduce frustration.…”

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

“…Another interesting open question is the existence and nature of the phase transitions in this model for R < −1/4. Unlike on the square lattice, the EFT found no LRO [27] but our recent MC study suggested a phase transition to a highly degenerate state consisting of frozen domains with the stripe-type AF ordering inside the domains separated by zero-energy domain walls [28]. A phase transition for R < −1/4 was very recently reported also by using the machine learning technique [30], however, the nature of the transition remains elusive.…”

“…One can notice that for R = −0.22 the pair of the curves splits in the vicinity of the expected transition temperature (anomalous decrease) and for R < −0.22 the temperature-decreasing curves do not join the temperature-increasing ones at low temperatures but rather follow different trajectories. In such a case, the energy corresponding of the temperature-decreasing branch is always higher and never reaches the expected ground-state value e GS = −3(2R + 1)/2 [27], denoted by the blackframed right-pointing triangles at T = 0. Therefore, apparently, in the temperaturedecreasing processes the system gets trapped in some rather stable, nevertheless, only metastable states.…”

“…Considering the amount of work done on the frustrated J 1 − J 2 model on the square lattice, it is surprising that the corresponding model on the honeycomb lattice has received much less attention [24][25][26][27][28][29][30]. In fact, due to the smaller coordination number the latter frustrated model might display even more interesting effects, similar to its Heisenberg counterpart [31,32].…”

“…In fact, due to the smaller coordination number the latter frustrated model might display even more interesting effects, similar to its Heisenberg counterpart [31,32]. The critical behavior of this model on the honeycomb lattice was studied by the EFT [27] and very recently also by interesting machine learning approaches [29,30]. Nevertheless, the order of the transition was only investigated in the former approach with not quite conclusive findings.…”