Ising Model
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An Ising Model is a mathematical model that ...
- Context:
- It can range from being a 1-D Ising Model, to being a 2-D Ising Model (such as a 2-D square-lattice Ising model), to being ...
- It can (typically) be used for modeling Ferromagnetism in statistical mechanics.
- See: Factor Graph, Mean Field, Spin Glass, Phase Transition, Mean Field Theory, Lattice (Group), Transfer-Matrix Method, Quantum Field Theory, Metropolis Algorithm, Quantum Annealing Algorithm, Undirected Graphical Statistical Model.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Ising_model Retrieved:2015-2-28.
- The Ising model named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice, allowing each spin to interact with its neighbors. The model allows the identification of phase transitions, as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. [1] The Ising model was invented by the physicist , who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model has no phase transition and was solved by himself in his 1924 thesis. [2] The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by . It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.
In dimensions greater than four, the phase transition of the Ising model is described by mean field theory.
- The Ising model named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice, allowing each spin to interact with its neighbors. The model allows the identification of phase transitions, as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. [1] The Ising model was invented by the physicist , who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model has no phase transition and was solved by himself in his 1924 thesis. [2] The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by . It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.
- ↑ See , Chapters VI-VII.
- ↑ Ernst Ising, Contribution to the Theory of Ferromagnetism
2000
- (Cipra, 2000) ⇒ Barry A. Cipra. (2000). “The Ising model is NP-complete." SIAM News, 33(6).
1998
- (Kadowaki & Nishimori, 1998) ⇒ T. Kadowaki and H. Nishimori. (1998). “Quantum annealing in the transverse Ising model" Phys. Rev. E 58, 5355