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The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field H = iθT∕2 with the “topological” angle θ and temperature T was investigated numerically. In order to treat such a complex-valued statistical weight, we employed the transfer-matrix method. As a probe to detect the order–disorder phase transition, we resort to an extended version of the fidelity F, which makes sense even for such a non-Hermitian transfer matrix. As a preliminary survey, for an intermediate value of θ, we investigated the phase transition via the fidelity susceptibility χF(θ). The fidelity susceptibility χF(θ) exhibits a notable signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility. Thereby, we analyze the end-point singularity of the order–disorder phase boundary at θ = π. We cast the χF(θ) data into the crossover-scaling formula with δθ = π − θ scaled carefully. Our result for the crossover exponent ϕ seems to differ from the mean-field and square-lattice values, suggesting that the lattice structure renders subtle influences as to the multi-criticality at θ = π.

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