According to Ray and Jan the cluster development in a spin glass can be described by calculating spin flip probabilities and by association of rarely flipping spins. We show

The factors that make certain magnetic materials behave similarly to corresponding Ising models are reviewed. Examples of extensively studied materials include Dy(C2H5SO4)3.9H2) (DyES), Dy3Al5O12 (DyAlG), DyPO4, Dy2Ti2O7, LiTbF4, K2CoF4, and Rb2CoF4. Various comparisons between theory and experiment for these materials are examined. The agreement is found to be generally very good, even when th...

Consider the nearest-neighbor Ising model on $$\Lambda _n:=[-n,n]^d\cap {\mathbb {Z}}^d$$ at inverse temperature $$\beta \ge 0$$ with free boundary conditions, and let $$Y_n(\sigma ):=\sum _{u\in \Lambda _n}\sigma _u$$ be its total magnetization. Let $$X_n$$ magnetization perturbed by a critical Curie–Weiss interaction, i.e., $$\begin{aligned} \frac{d F_{X_n}}{d F_{Y_n}}(x):=\frac{\exp [x^2/\le...

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev’s p-wave superconductor, which has application in fault-tolerant topological computing. Kitaev chain is an example a new class critical phenomena—the phase transition. Mapping Pauli’s spin operators spinless fermionic creation and annihilation by inverse Jordan-Wigner transformat...

The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and confinement. Here we discuss how Ising field theory also gives the simplest model for particle decay. The decay widths computed in this theory provide the obvious tes...