OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 2026 05 10 Investigation of Quantum Chaos in Local and Non-local Ising Models 10.57647/ijm2c.2027.1701.01 EN Reza Pirmoradian Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran Maryam Teymouri Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran Elham Sadoogh Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran Negar AbolghasemiAzad Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran https://orcid.org/0009-0003-6325-0648 Mohammad Reza Lahooti Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran Zahra MohammadAli Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran Journal Article 2026 05 10 Time New Roman 10 We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit integrable or chaotic dynamics contingent on interaction strengths and field parameters, systems with non-local interactions generally display a stronger propensity toward chaos, even when the non-local couplings are weak. By examining the distribution of energy level spacings through the level spacing ratio, we delineate the transition from integrable to chaotic regimes and characterize the emergence of quantum chaos in these systems. Our analysis demonstrates that non-local couplings facilitate faster operator spreading and more intricate dynamical behavior, enabling these systems to approach maximal chaos more readily than their local counterparts. Additionally, we analyze Krylov complexity as a dynamical probe of chaos, observing a characteristic peak followed by a plateau at late times in chaotic regimes. This behavior provides a quantitative means to distinguish between integrable and chaotic phases, with the growth rate and saturation level of the complexity serving as effective indicators. Our findings underscore the role of non-local interactions in accelerating the onset of chaos and modifying dynamical complexity in quantum spin chains.