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The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, 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 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 ...
For an Ising model on a 2d lattice, the critical temperature is =. In practice, the main difference between the Metropolis–Hastings algorithm and with Glauber algorithm is in choosing the spins and how to flip them (step 4). However, at thermal equilibrium, these two algorithms should give identical results.
Apparently independent of the work of Young and Elcock, Bortz, Kalos and Lebowitz [1] developed a KMC algorithm for simulating the Ising model, which they called the n-fold way. The basics of their algorithm is the same as that of Young, [8] but they do provide much greater detail on the method.
Exact diagonalization (ED) is a numerical technique used in physics to determine the eigenstates and energy eigenvalues of a quantum Hamiltonian.In this technique, a Hamiltonian for a discrete, finite system is expressed in matrix form and diagonalized using a computer.
A Boltzmann machine (also called Sherrington–Kirkpatrick model with external field or stochastic Ising model), named after Ludwig Boltzmann, is a spin-glass model with an external field, i.e., a Sherrington–Kirkpatrick model, [1] that is a stochastic Ising model. It is a statistical physics technique applied in the context of cognitive ...
The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose symmetry algebra is the Virasoro algebra with the central charge c = 1 2 {\displaystyle c={\tfrac {1}{2}}} .
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 ...