Prof. ZHANG Zhidong from the Institute of Metal Research, Chinese Academy of Sciences (IMR, CAS), has achieved another milestone in theoretical physics by successfully obtaining the exact solution of the three-dimensional (3D) Z₂ lattice gauge theory. This remarkable feat follows his earlier groundbreaking work in solving the century-old ferromagnetic 3D Ising model.

The new research findings have been published in the international academic journal Open Physics, under the title "Exact solution of the three-dimensional Z₂ lattice gauge theory".

Gauge theories are fundamental to understanding particle interactions. The Z₂ lattice gauge theory, despite being the simplest of its kind, retains essential features shared by the thepries govering electromagnetic, weak, and strong nuclear forces. However, solving it exactly in three dimensions has resisted an open challenge for decades.

The key breakthrough emerged from recognizing a profound mathematical connection between the 3D Z₂ lattice gauge theory and the 3D Ising model through duality – a relationship that allows translating problems between the two systems. By establishing this connection and building on his previous exact solution of the 3D Ising model, Prof. ZHANG derived the complete exact solution for the gauge theory.

For the first time, this solution provides, exact expressions for all fundamental properties including the partition function, critical point, and critical exponents. These exponents – numerical values characterizing phase transitions – were determined to be identical to those of the 3D Ising model, confirming they belong to the same universality class.

This work reveals the crucial role of non-trivial topological structures in determining the properties of interacting many-body systems. It also explains why previous approximate methods, such as series expansions and Monte Carlo simulations, inevitably introduced systematic errors – as they failed to capture these topological contributions.

The exact solution opens new possibilities for deeper understanding various physical phenomena, from quark confinement in particle physics to phase transitions in condensed matter systems. It also establishes a rigorous benchmark for testing computational methods and offers new insights into the mathematical structure of quantum field theories.