In this extended summary of a seminar presentation, the one- and two-dimensional Ising models are presented and main aspects such as phase transitions are discussed. Further the …

Two-dimensional Ising model shown as a lattice of interacting spins. The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a …

Ising, 2d XY, and 3d Ising models. These examples respectively illustrate the general features of the classical/quantum correspondence, a Berry phase term, and the role of gauge constraints.

2D Ising model: For two and higher dimensions, we can introduce islands of defects, which cost only at the boundaries, and are thus, proportional to the perimeter L = ε N 2, where 0 < ε < 1....

Sep 20, 2022 · In order to evaluate the main prediction (4.4.14) of the Weiss theory, let us now discuss the exact (analytical) and quasi-exact (numerical) results obtained for the Ising model, …

I will discuss the use of the Ising model as a simple model for a magnetic system and how to use it (paired with the Metropolis method) to detect/predict the magnetic properties of materials.

1D Ising model: It is equivalent to an easily solvable, non-interacting model. There is no spontaneous magnetization or phase transition, because each lattice site has too few …

Figures from Landau and Binder (LB), MC Simulations in Statistical Physics, 2000. Consider a lattice with L2 sites and their connectivity (e.g. a square lattice). Each lattice site has a single …

energy (5.3) defines the model known as Ising model. The free energy F can be obtained from the partition function (5.2) using free energy, internal energy, entropy, specific heat, magne …

Finite dimensional Ising models. No phase transition in 1D; Full solution of the 1D Ising model. What are the first two moments of the magnetization? Existence of a phase transition in the 2D …