Discrete Fields in Condensed Matter

Fundamental interactions, according to quantum field theory, are realized through the exchange of interaction quanta-packets of matter-energy with defined quantum numbers, namely momentum-energy, spin, electric charge, etc. They are discrete interactions, in contradistinction to the classical continuous picture. By a classical model of discrete interaction, we mean the replacement of the potential representative of the continuous interaction, by the exchange of, in an evident abuse of language, classical ?quanta?, little bits of well-defined amounts of energy-momentum. This classical quantum is emitted/absorbed in an instantaneous process caused also by the absorption/emission of a previous quantum. We intend to start a discussion about the formalism of discrete interactions in a non-relativistic regime, which is appropriate for dealing within condensed matter, and propose a model of two spin interacting, via Heisenberg Hamiltonian, where the exchange interaction is via a discreet field that will be discuss during the presentation where we will use the statistical physics to analyses the new terms that appear during the formalism.