Energy = 0

We mapped the phase spaces to complex networks in four models: antiferromagnets on triangular lattices at ground states and above ground states, six-vertex (spin ice) models, 1D and 2D lattice gases. Their phase-space networks share some common features including the Gaussian degree distribution, the Gaussian spectral density, and the small-world properties. The phase spaces exhibit unique self-similar properties. Models with long-range correlations in real space exhibit fractal phase spaces, while models with short-range correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of the untested assumptions in Tsallis nonextensive statistics even though Tsallis entropy does not apply to these systems. The network community analysis can be used to quantify the weak ergodicity. Models: 1. Antiferromagnet on triangular lattice (above the ground state