Classical and quantum energies for interacting magnetic systems

TL;DR

This paper explores classical and quantum interpretations of the leading term in the ground state energy expansion for spin systems in quantum electrodynamics, linking quantum results with classical physics laws.

Contribution

It introduces an operator $A_M$ that connects quantum and classical interpretations of the ground state energy in spin systems, highlighting its relation to ground state multiplicity.

Findings

The quadratic term in the ground state expansion can be interpreted classically and quantum mechanically.

The operator $A_M$ provides a bridge between quantum spin states and classical physics laws.

Connections between the ground state multiplicity and the operator $A_M$ are established.

Abstract

The purpose of this article is to give different interpretations of the first non vanishing term (quadratic) of the ground state asymptotic expansion for a spin system in quantum electrodynamics, as the spin magnetic moments go to $0$. One of the interpretations makes a direct link with some classical physics laws. A central role is played by an operator $A_M$ acting only in the finite dimensional spin state space and making the connections with the different interpretations, and also being in close relation with the multiplicity of the ground state.