- 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.
Andrew Elvey Price, A. Guttmann. Permutations sortable by deques and by two stacks in parallel. European Journal of Combinatorics, 59, 71-95, 2017. doi: 10.1016/j.ejc.2016.08.002.
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.
1978 Awarded Fulbright Senior Fellowship
2000 Fellow of the Australian Mathematical Society
2003 Centenary Medal
2007 Fellow of the Australian Academy of Technological Sciences and Engineering
2009 Fellow of the Society for Industrial and Applied Mathematics
2012 Awarded Australian Mathematical Sciences Institute (AMSI) Medal
2016 Awarded certificate as Most published author by Journal of Physics A.
2020 Member of the Order of Australia (AM).
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 CONWAY||""On the behaviour of self-avoiding walks and related problems""|
|Andrew ELVEY PRICE||""Selected problems in enumerative combinatorics: Permutation classes, random walks and planar maps.""|
|Will JAMES||"The enumeration of heaps and almost-convex polygons"|
|Andrew RECHNITZER||"Some problems in the counting of lattice animals, polyominoes, polygons and walks"|
|Andrew ROGERS||""Parallel algorithms for lattice enumeration problems""|
|Marcus VOEGE||""Topics in Statistical Mechanics: The n-friendly walker model and benzenoid systems""|
|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
|Robert BURSILL||""Loop-erased self-avoiding walks""|
|Mark WASSELL||""Estimating a critical exponent for the self-avoiding walk""|
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|