Context is 1D Ising model. Metropolis algorithm is utilized for simulate that model. Among all possible spins configurations (states) that algorithm generates only states by the desired Boltzmann probability.
Algorithm chooses spin at random and makes a trial flip. If trial satisfies certain conditions related to Boltzmann probability, flip is accepted. Otherwise flip is rejected and system is unchanged.
Describe "acceptance ratio" as a percentage of accepted trials. Simulation shows that acceptance ratio is higher on higher temperature (behave as increasing function of temperature).
Questions:
1. Is efficiency of algorithm related to acceptance ratio?
2. Why Metropolis algorithm is not efficient at low temperatures?