2012/09/30 by Ran Huang, Purushottam D. Gujrati
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Antiferromagnetism #Coordination number #Glass transition #Ideal (ethics) #Ising model #Lattice (music) #Material Dynamics and Properties #Monatomic ion #Square lattice #Supercooling #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0253-6102/64/3/345
published as Commun. Theor. Phys. 64 345 (2015) · 27 pages, 13 figures
arxiv created 2014/11/14 · openalex publication_date 2015/09/01 · arxiv updated 2016/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Two types of recursive lattices with the identical coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. A multi-branched structure of the 2-D plaquette model, which we introduced in this work, makes it possible to be an analog to the cubic lattice. Two solutions of each model can be found to exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices, e.g. the free energy, energy density, and entropy of the supercooled liquid, crystal, and liquid state of the model are calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance and multi-spins interactions are taken into consideration, and their effects on the thermal behavior are examined. The two lattices show comparable properties on the thermodynamics, which proves that both of them are practical to describe the regular 3-D case, especially to locate the ideal glass transition, while the 2-D multi-branched plaquette model is less accurate with the advantage of simpler formulation and less computation time consumption.