# Statistical Physics and Discrete Mathematics

Methods of statistical physics have been successfully used in recent years for a study of various topics in combinatorics and computer science. Particular topics of interest include: phase transitions in combinatorial structures, method of cluster expansions and their use for study of zeros of combinatorial polynomials, structures in perfect colourings of graphs.

## Sample publications:

- R. Kotecký, J. Salas, and A.D. Sokal. Phase Transition in the Three-State Potts Antiferromagnet on the Diced Lattice,
*Physical Review Letters*, 101(3), 2008, 030601. - R. Kotecký. Mathematics of Phase Transitions.
*Lecture Notes from the Summer School "Physics and Theoretical Computer Science From Numbers and Languages to (Quantum) Cryptography"*, Cargese, October 17 - 29, 2005, volume 7, NATO Security through Science Series: Information and Communication Security, eds. J.-P. Gazeau, J. Nesetril and B. Rovan, 2007.

- M. Biskup, C. Borgs, J.T. Chayes, R. Kotecký, and L. Kleinwaks. Partition Function Zeros at First-Order Phase Transitions: A General Analysis,
*Communications in Mathematical Physics*, 251(1): 79 - 131, October 2004. - R. Kotecký. Cluster Expansions,
*Encyclopedia of Mathematical Physics*, volume 1, pages 531 - 536, eds. J.-P. Francoise, G.L. Naber, and S.T. Tsou, Oxford, Elsevier, 2006. - D. Achlioptas, A. Coja-Oghlan. Algorithmic barriers from phase transitions.
*Proc. 49th FOCS (2008) 793-802.* - Michael Behrisch, A. Coja-Oghlan, Mihyun Kang. The order of the giant component of random hypergraphs.
*Random Structures and Algorithms 36 (2010) 149-184.*