# Markov-chain Monte Carlo methods in statistical mechanics

Statistical mechanics is that branch of mathematical physics which seeks to explain how macroscopic behaviour can emerge from the interactions between a large number of microscopic particles; in short, to explain how and why the sum is greater than its parts. Due to the complexity of such models, sophisticated computational algorithms are often required in order to make progress. Chief amongst such tools, are Markov-chain Monte Carlo methods. This project will devise, and rigorously analyse, Monte Carlo algorithms for studying discrete/combinatorial models in both equilibrium and non-equilibrium statistical mechanics.

## Related Publications

#### 2018

Elçi, E. Metin, Grimm J., Ding L., Nasrawi A., Garoni T. M., & Deng Y. (2018).  Lifted worm algorithm for the Ising model. Physical Review E. 97(4),  doi: 10.1103/PhysRevE.97.042126

#### 2016

Collevecchio, A., Garoni T. M., Hyndman T., & Tokarev D. (2016).  The worm process for the Ising model is rapidly mixing. Journal of Statistical Physics. 164(5), 1082-1102. doi: 10.1007/s10955-016-1572-2