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In statistical mechanics, the two-dimensional square lattice Ising model is a simple lattice model of interacting magnetic spins. The model is notable for having nontrivial interactions, yet having an analytical solution. The model was solved by Lars Onsager for the special case that the external magnetic field H = 0. [1]
The Hamiltonian of the one-dimensional Ising model on a lattice of L sites with free boundary conditions is = =, …, +, where J and h can be any number, since in this simplified case J is a constant representing the interaction strength between the nearest neighbors and h is the constant external magnetic field applied to lattice sites.
The Ising model is given by the usual cubic lattice graph = (,) where is an infinite cubic lattice in or a period cubic lattice in , and is the edge set of nearest neighbours (the same letter is used for the energy functional but the different usages are distinguishable based on context).
The Ising model is a mathematical model of ferromagnetism, in which the magnetic properties of a material are represented by a "spin" at each node in the lattice, which is either +1 or -1. The model is also equipped with a constant K {\displaystyle K} representing the strength of the interaction between adjacent nodes, and a constant h ...
The transverse field Ising model is a quantum version of the classical Ising model.It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the axis, as well as an external magnetic field perpendicular to the axis (without loss of generality, along the axis) which creates an energetic bias for one x-axis spin direction ...
The Ising model is the original model that Lee and Yang studied when they developed their theory on partition function zeros. The Ising model consists of spin lattice with N {\displaystyle N} spins { σ k } {\displaystyle \{\sigma _{k}\}} , each pointing either up, σ k = + 1 {\displaystyle \sigma _{k}=+1} , or down, σ k = − 1 {\displaystyle ...
It relates the free energy of a two-dimensional square-lattice Ising model at a low temperature to that of another Ising model at a high temperature. It was discovered by Hendrik Kramers and Gregory Wannier in 1941. [1] With the aid of this duality Kramers and Wannier found the exact location of the critical point for the Ising model on the ...
The Ising model, a mathematical model in statistical mechanics, is utilized to study magnetic phase transitions and is a fundamental model of interacting systems. [1] Constructing an irreducible Markov chain within a finite Ising model is essential for overcoming computational challenges encountered when achieving exact goodness-of-fit tests ...
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