Classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> spin liquid on the generalized four-color Kitaev model

While <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>U</a:mi><a:mo>(</a:mo><a:mn>1</a:mn><a:mo>)</a:mo></a:math> spin liquids have been extensively studied in both quantum and classical regimes, exact classical <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi mathvariant="double-struck">Z</b:mi><b:mn>2</b:mn></b:msub></b:math> 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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi mathvariant="double-struck">Z</d:mi><d:mn>2</d:mn></d:msub></d:math> spin liquids across a broad family of tricoordinated lattices. By formulating a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi mathvariant="double-struck">Z</f:mi><f:mn>2</f:mn></f:msub></f:math> 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. We complement our findings with Monte Carlo simulations, revealing a crossover from a high-temperature paramagnet to a low-temperature liquid phase characterized by residual entropy, classical <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi mathvariant="double-struck">Z</h:mi><h:mn>2</h:mn></h:msub></h:math> flux order, and diffuse spin structure factors.