• It is also known as mother of all thermal Monte Carlo algorithms.
• Three Crucial concepts are required to understand Metropolis or all kinds of thermal monte carlo simulation.
  1. Importance Sampling
  2. Detailed Balance
  3. Acceptance Ratios

• Once we have understood above concepts, the theory of Metropolis algorithm is as follows.
• The Metropolis algorithm was introduced by Nicolas Metropolis and his co-workers in a 1953 paper on simulations of hard-sphere gases (Metropolis et al. 1953).
• We will use this algorithm to find equilibration time, measurement of expectation values, and the calculation of errors.