The goal of this experiment was to create Monte Carlo simulations of the 1D and 2D Ising model. To accomplish this the Metropolis algorithm was implemented in MATLAB. The dependence of magnetization on temperature with and without an external field was calculated, as well as the dependence of the energy, specific heat, and magnetic susceptibility on temperature. The results of the 2D simulation...

This model was suggested to Ising by his thesis adviser, Lenz. Ising solved the one-dimensional model, ..., and on the basis of the fact that the one-dimensional model had no phase transition, he asserted that there was no phase transition in any dimension. As we shall see, this is false. It is ironic that on the basis of an elementary calculation and erroneous conclusion, Ising’s name has beco...

We study the conformal spectra of the critical square lattice Ising model on the Klein bottle andMöbius strip using Yang-Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang-Baxter techniques and functional equations can be used to st...

The scattering-matrix for planar Yang-Mills with N = 4 supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this note we define a map from the spectral variables x±, parameterizing the long-range magnon momenta, to couplings in a two-dimensional Ising model. Under this map integrability of planar N = 4 Yang-Mills becomes equivalent to the Yang...

Polynomial time reductions between problems have long been used to delineate problem classes. Simulation reductions also exist, where an oracle for simulation from some probability distribution can be employed together with an oracle for Bernoulli draws in order to obtain a draw from a different distribution. Here linear time simulation reductions are given for: the Ising spins world to the Isi...

There is evidence that the functional patterns of the brain observed at rest using fMRI are sustained by a structural architecture of axonal fiber bundles. As neuroimaging techniques advance with time, the relationship between structure and function has become the object of many studies in neuroscience. As recently suggested, the well-defined connectivity structure found in the brain can be use...

We study the performance of a Wolff-type embedding algorithm for RP σ-models. We find that the algorithm in which we update the embedded Ising model à la Swendsen-Wang has critical slowing-down as zχ ≈ 1. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain zχ ≈ 0. This shows that the Ising embedding encodes w...

We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the ...

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensiona...

Articles you may be interested in Social applications of two-dimensional Ising models Am. The critical temperature of two-dimensional and three-dimensional Ising models Am. The critical renormalized coupling constants in the symmetric phase of the three dimensional Ising model AIP Conf. We consider the diagonal susceptibility of the isotropic 2D Ising model for temperatures below the critical t...