Abstract

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 χ_F^(θ). The fidelity susceptibility χ_F^(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 χ_F^(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.

Graphical abstract

中文翻译：

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虚磁场下蜂窝格伊辛反铁磁体的保真度分析

摘要

数值研究了具有“拓扑”角θ和温度T的虚磁场H = iθT ∕ 2时的蜂窝格伊辛反铁磁体。为了处理这种复数值统计权重，我们采用了转移矩阵法。作为检测有序-无序相变的探针，我们求助于保真度F的扩展版本，即使对于这样的非Hermitian传输矩阵，它也有意义。作为初步调查，对于中间值θ，我们研究了通过保真度易感性的相转变χ _˚F^（θ）。保真度χ _˚F^（θ）表现出对临界比普通量词作为显着的签名如磁化率。因此，我们分析了θ = π时有序-无序相边界的端点奇点。我们铸χ _˚F^（θ）的数据与交叉的缩放式δθ = π - θ仔细缩放。我们对交叉指数结果φ似乎从平均场和正方形晶格值不同，这表明晶格结构呈现微妙的影响作为对多临界在θ =π。

图形概要