2017/12/11 by Ron Peled, Peled, Ron, Yinon Spinka +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1712.03699
openalex publication_date 2017/12/11 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28
We give a general condition for a discrete spin system with nearest-neighbor interactions on the ℤd lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic q-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for q≥ 4. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the known regime of the demixed phase in the lattice Widom-Rowlinson model.