Small-Network Approximations for Geometrically Frustrated Ising Systems
| Autor: | Bilin Zhuang, Courtney Lannert |
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| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Models
Molecular Spins Statistical Mechanics (cond-mat.stat-mech) Small systems FOS: Physical sciences Square-lattice Ising model Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Condensed Matter::Disordered Systems and Neural Networks Phase Transition Models Chemical Nonlinear Dynamics Lattice (order) Oscillometry Hexagonal lattice Ising model Computer Simulation Condensed Matter::Strongly Correlated Electrons Statistical physics Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths in frustrated Ising systems, we develop a method for obtaining first approximations to the energetic properties of frustrated two-dimensional Ising systems using small networks of less than 30 spins. These small networks allow much faster numerical simulations, and more importantly, analytical evaluations of their properties are numerically tractable. We choose Ising systems on the triangular lattice, the kagome lattice, and the triangular kagome lattice as prototype systems and find small systems that can serve as good approximations to these prototype systems. Through comparisons between the properties of extended models and small systems, we develop a set of criteria for constructing small networks to approximate general infinite two-dimensional frustrated Ising systems. This method of using small networks provides a different and efficient way to obtain a first approximation to the properties of frustrated spin systems. |
| Databáze: | OpenAIRE |
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