Topological Expression for Frustration in Antiferromagnetic Triangular Ising Model

Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

“…Hereafter, the crossover exponent φ is considered as an adjustable parameter, and the other indices, ẋ, α(θ) F , and ν, are fixed in prior to the scaling analyses as follows. According to the duality theory [26], the hexagonal-lattice Ising antiferromagnet at θ = π reduces to the triangular-lattice antiferromagnet, and the uniform-susceptibility and correlation-length exponents are given by γaf = 3/2 and ν = 1, respectively [40]. Notably enough, through the duality, the frustrated (non-bipartite lattice) antiferromagnet comes out from the seemingly non-frustrated magnet, albeit with the imaginary magnetic field mediated.…”

“…In this paper, we demonstrate that the complex-valued nonsymmetric T , namely, the honeycomb-lattice case, is also tractable with the simulation scheme. It is anticipated that the criticality of the honeycomblattice model is not identical to that of the square-lattice model, because the former possesses the duality [26,27,28] at a finely-tuned value of the imaginary magnetic field.…”

“…with the "topological" angle θ, and temperature T , and likewise, the reduced coupling constant K = J/T is introduced. A schematic drawing of the phase diagram [26,27,28,29,30,31] is presented in Fig. 1 (a).…”

“…So far, the model (4) has been investigated by means of the partition-function zeros [29], albeit with an emphasis on the real-H-driven criticality. Additionally, rigorous information in terms of the duality theory [26,27,28,30,31] is available at θ = π. In fairness, it has to be mentioned that the square-lattice counterpart has been investigated with the partition-function-zeros [32], series-expansion [33], and exact-diagonalization [25] methods in order to surmount the severe sign problem due to the imaginary magnetic field [34].…”

“…On the contrary, the above mentioned numerical results [32,33,25] for the square-lattice model indicate a concavely-curved phase boundary with φ > 1. Because the honeycomb-lattice antiferromagnet at θ = π is under the reign of the duality theory [26,27,28,30], the end-point singularity φ should reflect its peculiar characters. The aim of this paper is to explore φ quantitatively by casting the fidelity-susceptibility data into the crossoverscaling theory [36,37]; a key ingredient is that the probe χ (θ) F exhibits a notable singularity at the end-point θ = π.…”