# WKB Approximation

# Ising Model and Simulation

The Isinig model is a famous and applicable model in the statistical mechanics. In this project, I propose to consider the Ising model and its computational simulation. In this text, I try to review the main idea of the Ising model and Metropolis algorithm, the computational approach to this problem. Finally, I report the result of my own simulation and compare its results with analytical solution as a conclusion.

# Heisenberg Model

In this research, we try to calculate analytically eigenvalues and eigenvectors of finite chain with 5 1⁄2-spin particles Heisenberg model. We drove eigenfuctions for closed chain. After that we renormalized the result for interaction between chains for zero temperature. Finally according to self similarity, fix points were found from effective renormalization energy.

# Correspondence Principle

Correspondence principle is considering the history of scientific theories as a continuum process which the new theories are the result of former theories. First, this principle is introduced as independent basic in order to interpret quantum theory. After that, it gets attention in all of science areas and specially physics.

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