Exact Calculation of Antiferromagnetic Ising Model on an Inhomogeneous Surface Recursive Lattice to Investigate Thermodynamics and Glass Transition on Surface/Thin Film  

作　　者：黄然 Purushottam D.Gujrati 

机构地区：[1]State Key Laboratory of Microbial Metabolism and School of Life Sciences and Biotechnology,Shanghai Jiao Tong University [2]Department of Physics,University of Akron

出　　处：《Communications in Theoretical Physics》2017年第1期111-126,共16页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No.11505110;Shanghai Pujiang Talent Program under Grant No.16PJ1431900;the China Postdoctoral Science Foundation under Grant No.2016M591666

摘　　要：An inhomogeneous 2-dimensional recursive lattice formed by planar elements has been designed to investigate the thermodynamics of Ising spin system on the surface/thin film. The lattice is constructed as a hybrid of partial Husimi square lattice representing the bulk and 1D single bonds representing the surface. Exact calculations can be achieved with the recursive property of the lattice. The model has an anti-ferromagnetic interaction to give rise to an ordered phase identified as crystal, and a solution with higher energy to represent the amorphous/metastable phase.Free energy and entropy of the ideal crystal and supercooled liquid state of the model on the surface are calculated by the partial partition function. By analyzing the free energies and entropies of the crystal and supercooled liquid state,we are able to identify the melting and ideal glass transition on the surface. The results show that due to the variation of coordination number, the transition temperatures on the surface decrease significantly compared to the bulk system.Our calculation qualitatively agrees with both experimental and simulation works on the thermodynamics of surfaces and thin films conducted by others. Interactions between particles farther than the nearest neighbor distance are taken into consideration, and their effects are investigated.An inhomogeneous 2-dimensional recursive lattice formed by planar elements has been designed to investigate the thermodynamics of Ising spin system on the surface/thin film. The lattice is constructed as a hybrid of partial Husimi square lattice representing the bulk and 1D single bonds representing the surface. Exact calculations can be achieved with the recursive property of the lattice. The model has an anti-ferromagnetic interaction to give rise to an ordered phase identified as crystal, and a solution with higher energy to represent the amorphous/metastable phase.Free energy and entropy of the ideal crystal and supercooled liquid state of the model on the surface are calculated by the partial partition function. By analyzing the free energies and entropies of the crystal and supercooled liquid state,we are able to identify the melting and ideal glass transition on the surface. The results show that due to the variation of coordination number, the transition temperatures on the surface decrease significantly compared to the bulk system.Our calculation qualitatively agrees with both experimental and simulation works on the thermodynamics of surfaces and thin films conducted by others. Interactions between particles farther than the nearest neighbor distance are taken into consideration, and their effects are investigated.

关 键 词：critical temperature ideal glass transition Ising model Husimi lattice SURFACE thin film 

分 类 号：O469[理学—凝聚态物理]