Mutual information in interacting spin systems

TL;DR

This thesis investigates phase transitions in ferromagnetic spin systems at finite temperature using mutual information from information theory, extending analysis beyond ground states to thermal states in classical and quantum models.

Contribution

It introduces the use of mutual information to analyze finite-temperature phase transitions in interacting spin systems, bridging classical and quantum models.

Findings

Mutual information effectively characterizes phase transitions.

Finite-temperature analysis reveals new insights into spin system behavior.

Classical and quantum models show distinct mutual information patterns.

Abstract

This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting spins. Quantum information theory often focuses on the ground state of such systems; we will however be interested in what happens at finite temperature. Using mutual information, which can be seen as a generalization of entanglement entropy to the finite-temperature case, we can study the different phases occurring in these models, and in particular the phase transitions between those. We examine broadly two different classes of models: classical spins on two-dimensional lattices, and fully-connected models of quantum-mechanical spin-1/2 particles. (Abstract abridged.)