Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices

TL;DR

This study uses Monte Carlo simulations to explore the complex phase behavior of a frustrated Ising model on generalized triangular lattices, revealing multiple ground states, phase transitions, and the role of residual entropy.

Contribution

It provides a detailed Monte Carlo analysis of the frustrated $J_1$-$J_2$ Ising model on two types of generalized triangular lattices, identifying novel ground states and phase transition characteristics.

Findings

Identified super-antiferromagnetic stripe states in GTL1.

Observed ferrimagnetic and partial spin liquid states in GTL2.

Mapped finite-temperature phase diagrams showing different transition types.

Abstract

We investigate the frustrated $J_1$-$J_2$ Ising model with nearest-neighbor interaction $J_1$ and next-nearest-neighbor interaction $J_2$ in two kinds of generalized triangular lattices (GTLs) employing the Wang--Landau Monte Carlo method and finite-size scaling analysis. In the first GTL (GTL1), featuring anisotropic properties, we identify three kinds of super-antiferromagnetic ground states with stripe structures. Meanwhile, in the second GTL (GTL2), which is non-regular in next-nearest-neighbor interaction, the ferrimagnetic 3$\times$3 and two kinds of partial spin liquid ground states are observed. We confirm that residual entropy is proportional to the number of spins in the partial spin liquid ground states. Additionally, we construct finite-temperature phase diagrams for ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. In GTL1, the transition into the ferromagnetic phase is continuous, contrasting with the first-order transition into the stripe phase. In GTL2, the critical temperature into the ferromagnetic ground state decreases as antiferromagnetic next-nearest-neighbor interaction intensifies until it meets the 3$\times$3 phase boundary. For intermediate values of the next-nearest-neighbor interaction, two successive transitions emerge: one from the paramagnetic phase to the ferromagnetic phase, followed by the other transition from the ferromagnetic phase to the 3$\times$3 phase.