We review the development of Monte Carlo algorithms for the simulation of the Ising model with local dynamics. The multi lattice coding algorithm for the pure and for the site-disordered Ising model is described in detail. Application of these algorithms on fast vector computers have led to new progress concerning the critical dynamics of the pure Ising model leading to the critical exponent z ...

We discuss the dynamics of the Ising model as a computational mesoscopic system. The simplicity of the Ising model allows a Hamiltonian dynamics to be developed from renormalization group theory considerations for the model which is not overly complicated and preserves a close connection with thermodynamics. At the same time, the additional structure gives the potential for application to neura...

The partition function of a quantal spin system is expressed by that of the Ising model, on the basis of the generalized Trotter formula. Thereby the ground state of the d-dimensional Ising model with a transverse field is proven to be equivalent to the (d+ 1) -dimensional Ising model at finite temperatures. A general relationship is established between the two partition functions of a general ...

A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lat...

A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lat...

1. Inference of couplings and of their accuracy within the inverse Ising model (page 2) 2. Limitations of the Ising model: higher-order correlations and couplings (page 7) 3. Algorithm for the Inverse Integrate-and-Fire Problem (page 11) 4. On Cross-correlograms: Analysis of Data, Relationship with Couplings, and Simulations (page 14) 5. Correspondence between Integrate-and-Fire and Ising Inver...

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of ar...

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of ar...

1 The Ising Model The Ising Model is a simple model of a solid that exhibits a phase transition resembling ferromagnetism. In this model, a “spin direction” is assigned to each vertex on a graph. The standard Hamiltonian for an Ising system includes only nearest-neighbor interactions and each spin direction may be either “up” (+1) or “down” (-1), though generalized models may include long-range...