Useful nucleus said:A quick and easy to follow guide is to watch lecture 17 and 18 from the course taught at MIT by Ceder and Marzari. Here is a link:
http://ocw.mit.edu/courses/material...aterials-sma-5107-spring-2005/video-lectures/
If you are keen on learning , start by Metropolis original paper! It is also readable and very informative:
http://jcp.aip.org/resource/1/jcpsa6/v21/i6/p1087_s1
Then when the time is ripe you can consult "understanding Molecular Simulation" This book has actually some algorithms and pseudo-code:
https://www.amazon.com/dp/0122673514/?tag=pfamazon01-20
The Metropolis algorithm is a computational method used to simulate the behavior of a physical system, particularly in statistical mechanics and molecular dynamics. It is used to generate samples from a probability distribution that is difficult to sample directly.
The Metropolis algorithm works by simulating the evolution of a system through a series of steps. At each step, a new configuration or state is proposed and then accepted or rejected based on a probability ratio. This ratio takes into account both the energy of the proposed state and the energy of the current state.
The Metropolis algorithm is important in physics because it allows us to study complex systems that are difficult to analyze analytically. It is particularly useful in studying phase transitions and critical phenomena, as well as in simulating the behavior of molecules and atoms in a system.
One limitation of the Metropolis algorithm is that it relies on the ability to propose new configurations of the system, which can be challenging for highly complex systems. It also requires a large number of steps to accurately sample the probability distribution, which can be computationally expensive.
The Metropolis algorithm is used in a variety of real-world applications, including materials science, chemistry, and biophysics. It is also widely used in machine learning as a method for optimizing parameters in models. Additionally, it has been used in computer simulations of physical systems, such as the Ising model in statistical mechanics.