Two exactly soluble lattice models in three dimensions

TL;DR

This paper reviews the exact solutions of two three-dimensional lattice models, highlighting progress and potential future breakthroughs in solving complex 3D lattice systems.

Contribution

It presents the first exact solutions of two 3D lattice models using combinatorial and transfer matrix methods, paving the way for future research.

Findings

Exact solutions for two 3D lattice models obtained.

Demonstrates the effectiveness of combinatorial and transfer matrix approaches.

Provides insights into potential future solutions for complex 3D systems.

Abstract

As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three dimensions obtained using the conventional combinatorial and transfer matrix approaches.