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

Abstract

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 alpha and of the universal amplitude ratio Delta = A_+/A_-, within the 3.5% and 7% of the Monte Carlo predictions, respectively.

arXiv comment18 pages, 1 figure

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Cited by in corpus (4)

• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Potts model on recursive lattices: some new exact results
• Duality and Fisher zeros in the 2D Potts model on square lattice
• Universal Amplitude Ratios in the Ising Model in Three Dimensions