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In this paper, we explore the stability of the energy landscape of an Ising Hamiltonian when subjected to two kinds of perturbations: a perturbation on the coupling coefficients and external fields, and a perturbation on the underlying graph structure. We give sufficient conditions so that the ground states of a given Hamiltonian are stable under perturbations of the first kind in terms of order preservation. Here by order preservation we mean that the ordering of energy corresponding to two spin configurations in a perturbed Hamiltonian will be preserved in the original Hamiltonian up to a given error margin. We also estimate the probability that the energy gap between ground states for the original Hamiltonian and the perturbed Hamiltonian is bounded by a given error margin when the coupling coefficients and local external magnetic fields of the original Hamiltonian are i.i.d. Gaussian random variables. In the end we show a concrete example of a system which is stable under perturbations of the second kind.
We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energ
We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{x,y} = J(|x-y|)equiv frac{1}{|x-y|^{2-alpha}}$ with $alpha in [0, 1)$,
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the reg
We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $lambda$ generalized
We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant for the ave