- Critical Phenomena (phase transitions)
- Exact solutions of lattice models
- Statistical Mechanics
- Enumerative combinatorics
- Mathematical Physics
N. Beaton, A. Guttmann, I. Jensen. Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents. Journal of Physics A: Mathematical and Theoretical, 53, 165002 (20pp), 2020. doi: 10.1088/1751-8121/ab7ad1.
A. Guttmann, EJ Janse van Rensburg, I. Jensen, S. Whittington. Polygons pulled from an adsorbing surface. Journal of Physics A: Mathematical and Theoretical, 51, 074001 (30pp), 2018. doi: 10.1088/1751-8121/aaa3b9.
N. Beaton, A. Guttmann, AR Conway. On consecutive pattern-avoiding permutations of length 4, 5 and beyond. Discrete Mathematics and Theoretical Computer Science, 19, 2018.
Andrew R Conway, A. Guttmann, P. Zinn-Justin. 1324-avoiding permutations revisited. Advances in Applied Mathematics, 96, 312-333, 2018. doi: 10.1016/j.aam.2018.01.002.
A. Elvey Price, AJ Guttmann, A. Guttmann. Permutations sortable by two stacks in series. Advances in Applied Mathematics, 83, 81-96, 2017. doi: 10.1016/j.aam.2016.09.003.
My research interests are in equilibrium statistical mechanics in general, and more particularly in discrete models of phase transitions. As these are often equivalent to a combinatorial problem, I am equally interested in the relevant combinatorics, and the connection between the two. Additionally, I am regularly looking for new ways to count the underlying graphs efficiently. This leads me into a study of algorithmic complexity.
Past Postgraduate Supervision
|Nicholas BEATON||"Combinatorics of Lattice Paths and Polygons"|
|Debra BENNETT-WOOD||"Numerical studies of Self-avoiding walks"|
|Yao-ban CHAN||"Selected problems in lattice statistical mechanics"|
|Andrew ELVEY PRICE|
|Will JAMES||"The enumeration of heaps and almost-convex polygons"|
|Robin LANGER||"Symmetric functions and Macdonald polynomials"|
|Andrew RECHNITZER||"Some problems in the counting of lattice animals, polyominoes, polygons and walks"|
|Jason WHYTE||"Global a priori identifiability of biomolecular interaction models in flow-cell optical biosensor experiments"|
|Henry (Ling Heng) WONG||"Topics on Lattice Models in Statistical Mechanics"|
Past Honours & MSc Students
Recent Grant History
|2014 - 2016||ARC||Discovery||Advanced algorithms for statistical mechanical models (080078)|
|2012 - 2014||ARC||Discovery||Critical behaviour of lattice models of spin systems|
|2010 - 2012||ARC||Discovery||Green functions, correlation functions and differential equations|
|2006||Szekeres Medal||Australian Mathematical Society|
|2005||Lyle Medal||Australian Academy of Science|
|2004||B H Neumann||Australian Mathematics Trust|
|2002||Fellow of The Australian Academy of Science||Australian Academy of Science|
|2000||Centenary Medal||Australian Government|
|1998||Hannan Medal||Australian Academy of Science|