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arXiv:2509.11437 · Physica A Statistical Mechanics and its Applications

The phase transitions of the frustrated J1-J2 Ising model on the honeycomb lattice

Shang-Wei Li, Yuan-Heng Tseng, Fu-Jiun Jiang

Published Sep 5, 2026• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2026.132016

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Using the density matrix renormalization group on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor (J1=1) and frustrating second-neighbor (J2>0) interactions. For the intermediate frustration regime 0.22≲J2≲0.36, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S(z)S(z) interactions in the Hamiltonian. Surrounding this phase as a function of J2 are antiferromagnetic phases with the moments pointing in the x-y plane for small J2 and a close competition between an x-y plane magnetic collinear phase and a dimer phase for large values of J2. We do not find any spin-liquid phases in this model.
Meandering stripes in the frustrated J1J_1J1​-J2J_2J2​ Ising model on the honeycomb lattice
We study the frustrated J1J_1J1​-J2J_2J2​ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at J1=1J_1=1J1​=1 and strong antiferromagnetic next-nearest-neighbor interactions, i.e., J2≤−1/4J_2 \leq -1/4J2​≤−1/4. Little is known for this range of J2J_2J2​, whereas for less negative values of J2J_2J2​ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for J2=−0.5J_2 = -0.5J2​=−0.5 and J2=−1J_2 = -1J2​=−1 is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For J2=−1/4J_2=-1/4J2​=−1/4 we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate S(T=0)/N=0.230 960 93(14)S(T=0)/N = 0.230\,960\,93(14)S(T=0)/N=0.23096093(14) in the thermodynamic limit N→∞N\rightarrow\inftyN→∞.
We study the nearest-neighbor exchange (J1{J}_{1}J1​) and second-nearest-neighbor exchange (J2{J}_{2}J2​) XYXYXY antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice XYXYXY N\'eel order at small J2{J}_{2}J2​ vanishes at ${J}_{2}/{J}_{1}=0.22\ifmmode\pm\else\textpm\fi{}0.01$ in agreement with results from density matrix renormalization group (DMRG) studies. Near the transition, we find evidence for an approximate emergent symmetry between XYXYXY and Ising degrees of freedom, namely the nearest-neighbor Ising and XYXYXY spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating XYXYXY and Ising orders. At still larger J2/J1{J}_{2}/{J}_{1}J2​/J1​ the columnar and dimer energies are found to be nearly degenerate. At even larger J2{J}_{2}J2​ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.