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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).
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 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}}} .
In the Ising model, we have say N particles that can spin up (+1) or down (-1). Say the particles are on a 2D grid. We label each with an x and y coordinate. Glauber's algorithm becomes: [3] Choose a particle , at random. Sum its four neighboring spins.
In d=2, the two-dimensional critical Ising model's critical exponents can be computed exactly using the minimal model,. In d=4, it is the free massless scalar theory (also referred to as mean field theory). These two theories are exactly solved, and the exact solutions give values reported in the table.
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 ...
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 2D ising model describes the behavior of FePS 3, [4] CrI 3. [ 2 ] and Fe 3 GeTe 2 , [ 7 ] while Cr 2 Ge 2 Te 6 [ 1 ] and MnPS 3 [ 14 ] behaves like isotropic Heisenberg model. The intrinsic anisotropy in CrI 3 and Fe 3 GeTe 2 is caused by strong spin–orbit coupling , allowing them to remain magnetic down to a monolayer , while Cr 2 Ge 2 ...