Emeritus Professor Anthony (Tony) GUTTMANN

Emeritus Professor (Associate) / Professor

School of Mathematics and Statistics

  • Room: G55
  • Building: Peter Hall Building
  • Campus: Parkville

Research Interests

  • Critical Phenomena (phase transitions)
  • Exact solutions of lattice models
  • Statistical Mechanics
  • Enumerative combinatorics
  • Mathematical Physics

Research Groups

Recent Publications

  • 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.

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Extra Information

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

Name Thesis title
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"
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

Name Project title

Recent Grant History

Year(s) Source Type Title
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


Year Name Organisation
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