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

TL;DR

This paper investigates the Fisher zeros distribution in the 3D Ising model using the Kallen-Lehmann approach, revealing a cusp phenomenon that improves the model's agreement with Monte Carlo results and enhances understanding of critical behavior.

Contribution

It introduces a novel analysis of Fisher zeros in the 3D Ising model, demonstrating how a cusp in the distribution improves the Kallen-Lehmann approach's accuracy.

Findings

Identification of a cusp in Fisher zeros distribution near the critical point.

Enhanced agreement with Monte Carlo data at high and low temperatures.

Accurate predictions of critical exponent alpha and amplitude ratio within 7%.

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.