Fisher zeros in the Kallen–Lehmann approach to 3D Ising model

The distribution of the Fisher zeros in the Kallen–Lehmann approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen–Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α   and of the universal amplitude ratio Δ=A+/A−Δ=A+/A−, within the 3.5% and 7% of the Monte Carlo predictions, respectively.