Tensor network investigation of the hard-square model

Using the corner-transfer matrix renormalization group to contract tensor network that describes its partition function, we investigate nature of phase transitions hard-square model, one exactly solved models statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess power networks such models, and probe 2D classical analog a 1D quantum model hard-core bosons recently attracted significant attention in context experiments on chains Rydberg atoms. Accordingly, concentrate two planes 3D parameter space spanned by activity coupling constants diagonal directions. We first only case studied so far with Monte Carlo simulations, opposite constants. confirm that, away not too from 3-state Potts point, transition out period-3 appears be unique Huse-Fisher chiral universality class, albeit significantly different exponents as compared Carlo. also identify additional reported Lifshitz disorder line, Ising large enough activity. To make contact atoms, then turn plane where ferromagnetic kept fixed, show resulting diagram very similar, difference being becomes first-order through tricritical agreement Baxter's prediction this should contain remarkable, almost quantitative version model.