Self-similarity of phase-space networks of frustrated spin models and lattice gas models.

We studied the self-similar properties of the phase spaces of two frustrated spin models and two lattice gas models. The two frustrated spin models were (1) the antiferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. Their phase spaces were mapped to networks so that the fractal analysis of complex networks can be applied. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of the untested assumptions in Tsallis nonextensive statistics. All the phase spaces have power-law "mass" -radius relations that reflect the local self-similar structures.