Duality Between Spin Networks and the 2D Ising Model

Duality of the 2D Nonhomogeneous Ising Model on the Torus

Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical boundary conditions along the cycles of the torus is expressed through some specific combination of the partition functions of the model on the original lat...

Efficient Parallelization of 2D Ising Spin Systems

(Abstract) The problem of efficient parallelization of 2D Ising spin systems requires realistic algorithmic design and implementation based on an understanding of issues from computer science and statistical physics. In this work, we not only consider fundamental parallel computing issues but also ensure that the major constraints and criteria of 2D Ising spin systems are incorporated into our ...

Duality and even number spin-correlation functions in the Two dimensional square lattice Ising model

The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature (T > Tc) expressions for these correlation functions are transformed into the low temperature (T < Tc) expressions under this duality transformation. PACS: 05.70.Jk The two dimensional Ising model remains one of ...

Structure-Function Relationship of the Brain: A comparison between the 2D Classical Ising model and the Generalized Ising model

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...

The solution of the 2D Ising model