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 consists of discrete variables that represent magnetic dipole moments of atomic “spins” that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.

Ising model was first exploited for investigating spontaneous magnetization in ferromagnetic film (i.e. magnetization in the absence of external magnetic field). An example case of Ising model using metropolis algorithm is shown in Figure 3.

The importance of the two-dimensional Ising model in a magnetic field is that it is the simplest system where this relationship may be concretely studied. We here review the advances made in this study, and concentrate on the magnetic susceptibility which has revealed an unexpected natural boundary phenomenon.

Hamiltonian of the Ising Model are the individual spins on each of the lattice sites. The first sum is over all pairs of neighboring lattice sites (a.k.a. bonds); it represents the interactions between spins.

The Ising model Ferromagnetism arises when a collection of atomic spins align such that their associated magnetic moments all point in the same direction, yielding a net magnetic moment which is macroscopic in size. The simplest theoretical description of ferromagnetism is called the Ising model.

Ising model. The term spin” and magnetic eld” in the Ising model originate from its initial application to the phenomenon of spontaneous magnetization in ferromagnetic materials such as iron. Each iron atom has a unpaired electron and hence a net spin (or magnetic moment). At low

De/fnition of Ising model Ising (Z. Physik, 31, 253, 1925) introduced a model consisting of a lattice of [&spin&]” variablessi, which can only take the values +1 (“) and1 (#). Every spin interacts with its nearestneighbors (2 in 1D) as well as with an external magnetic eldh. The Hamiltonian1of the Ising model is

The Ising Model is a mathematical model that doesn’t correspond to an actual physical system. It’s a huge (square) lattice of sites, where each site can be in one of two states. We label each site with an index , and we call the two states and .