A computational phase diagram for the transverse field Ising model

We study the transverse field Ising model, defined by the Hamiltonian $H =\frac{1}{2}\sum_{i, j\in [n]} J_{ij} Z_i Z_j +\sum_{i=1}^n h_i^z Z_i + η\sum_{i} X_i$ where $J $ is the symmetric interaction matrix, and $η$ is the transverse field strength. Let $Δ(J)=λ_{\max}(J)-λ_{\min}(J)$ be the spectral