Spin liquids are strongly correlated systems where magnetic moments do not show conventional order, even at the lowest temperatures. However, not all spin liquids are alike. The particular form of fluctuations, whether classical or quantum, leads to emergent phenomena such as topological order, emergent gauge fields, and fractionalized particles, which can ultimately be used to characterize and define their nature. While U(1) spin liquids have been extensively studied in both quantum and classical regimes, exact classical ℤ₂ spin liquids arising from models with nearest-neighbor, bilinear spin interactions are still rare.
In this Letter, we explore the four-color Kitaev model as a minimal model for stabilizing classical Z2 spin liquids across a broad family of tricoordinated lattices. By formulating a ℤ₂ lattice gauge theory, we identify this spin liquid as being described by an emergent Gauss’s law with effective charge-2 condensation, and deconfined fractionalized bond-charge excitations. Our work open the door to the study of a new type of spin liquid on a broad family of tricoordinate lattices, offering a new route to realize spin liquids in real materials in both two and three dimensions.

This work was published as Han Yan and Rico Pohle, “Classical ℤ₂ spin liquid on the generalized four-color Kitaev model”,
Phys. Rev. Research 7, L012052 (2025).