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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 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 quantum clock model is a quantum lattice model. [1] It is a generalisation of the transverse-field Ising model.It is defined on a lattice with states on each site. The Hamiltonian of this model is
Compute the change in energy if the spin x, y were to flip. This is =, (see the Hamiltonian for the Ising model). Flip the spin with probability / (+ /) where T is the temperature. Display the new grid. Repeat the above N times.
Because the Heisenberg Hamiltonian presumes the electrons involved in the exchange coupling are localized in the context of the Heitler–London, or valence bond (VB), theory of chemical bonding, it is an adequate model for explaining the magnetic properties of electrically insulating narrow-band ionic and covalent non-molecular solids where ...
The Jordan–Wigner transformation is often used to exactly solve 1D spin-chains such as the Ising and XY models by transforming the spin operators to fermionic operators and then diagonalizing in the fermionic basis. This transformation actually shows that the distinction between spin-1/2 particles and fermions is nonexistent.
The Bogoliubov inequality, shown above, can be used to find the dynamics of a mean field model of the two-dimensional Ising lattice. A magnetisation function can be calculated from the resultant approximate free energy. [9] The first step is choosing a more tractable approximation of the true Hamiltonian.
In statistical physics, the classical Heisenberg model, developed by Werner Heisenberg, is the = case of the n-vector model, one of the models used to model ferromagnetism and other phenomena. Definition