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High-fugacity expansion, Lee-Yang zeros, and order-disorder transitions in hard-core lattice systems. (English) Zbl 1400.82041

Summary: We establish existence of order-disorder phase transitions for a class of “non-sliding” hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a finite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee-Yang zeros lie in an annulus with finite positive radii.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
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