Spin Systems and the Green Functions Method

В. Л. Аксенов, Jürgen Schreiber

D. I. Kadyrov

Tetsuo Matsui

The Green's-function method is employed to study the two-dimensional system of classical $\mathrm{O}(N)$-vector spins. The second-order double-time retarded Green's functions of the corresponding quantum Hamiltonian system on a one-dimensional lattice are decoupled approximately in a selfconsistent manner. The expressions for the mass gap and the spin-correlation function thus obtained reproduce the known exact results in the large-$N$ limit and in the strong-coupling region. Some directions are discussed to improve the present method in the region of weak coupling with $N$ not large.

Anonymous, Takao Morinari

A wide range of analytical and numerical methods are available to study quantum spin systems. However, the complexity of spin correlations and interactions limits their applicability to specific temperature ranges. The analytical approach utilizing Green's function has proved advantageous, as it allows for formulation without restrictions on the presence of long-range order and facilitates estimation of the spin excitation spectrum and thermodynamic quantities across the entire temperature range. In this work, we present a generalized formulation of the Green's function method that can be applied to diverse spin systems. As specific applications, we consider the hypercubic lattice and the $J_1$-$J_2$ model. For the cubic lattice case, the Green's function approach provides a good estimation for the transition temperature. Regarding the $J_1$-$J_2$ model, we include nematic correlations in the analysis and find no signature of such correlations, though accurate numerical calculations are required in the presence of strong frustration. Although our focus is on the spin one-half antiferromagnetic Heisenberg model on an arbitrary lattice, the Green's function approach can be generalized to incorporate other interactions and higher spin values.

G. Ramachandran, K. S. Mallesh

B. A. Shiwai, Michael G Cottam

Abstract A Green function equation‐of‐motion method is employed to calculate the dynamic properties of a semi‐infinite spin system (or pseudo‐spin system) described by the Ising model in a transverse field. The excitations of the system are shown to be the bulk and surface spin waves, and the Green functions are employed to evaluate their spectral intensities and integrated power factors at temperatures above the transition temperature Tc. Some numerical examples are also included.