Expansion methods in statistical mechanics
Successes, limitations, perspectives and alternatives

July 2–3, 2015; Utrecht University

Funded by STAR cluster and Utrecht University


Expansion techniques have been at the center of the theory of statistical mechanical system almost from the creation of the discipline. The virial expansion, proposed at the beginning of the XX century, is a central tool for the study of real fluids. The cluster expansion, introduced a couple of decades later, was originally conceived as an auxiliary expansion allowing the determination from first principles of the virial coefficients. The expansion, however, acquired a relevance of its own, when it was formalised in the early seventies as the main tool for perturbative arguments both in field theory and in rigorous statistical mechanics. The surge of these two areas of research triggered the development of other expansion approaches on random geometric objects, in particular the lace expansion which is the subject of much current research activity. The last decade has witnessed a number of advances in the theory and application of these techniques. The study of lace expansions has reached a new level of sophistication that has lead to important refinements and extensions. Cluster expansions have benefited from new summability approaches that led to improved convergence conditions. More recently, researchers have turned to the virial expansion, whose standing rigorous results dated from more than 40 years ago. The proposed workshop intends to exploit this promissory state of affairs by bringing together people involved in these recent advances for two days of reflection and exchange of ideas.

The workshop is free and open to all.


  • Stein Bethuelsen (Leiden)
  • Aernout van Enter (Groningen)
  • Tyler Helmuth (Brown)
  • Christoph Hofer-Temmel (Den Helder)
  • Tim Hulshof (Eindhoven)
  • Sabine Jansen (Bochum)
  • Roman Kotecký (Charles and Warwick)
  • Aldo Procacci (Minas Gerais)
  • Elena Pulvirenti (Leiden)
  • Stephen Tate (Imperial College)
  • Dimitrios Tsagkarogiannis (Sussex)
  • Daniel Ueltschi (Warwick)



The workshop will take place at the Buys Ballotgebouw, Princetonplein 5, De Uithof, Utrecht, room BBG-165.
For instructions and maps see here.

Thursday 2

09:00–09:10 R. Fernández: Welcoming message
09:15–10:00 Stephen Tate: Tree Partition schemes in the virial expansion
10:15–11:00 Sabine Jansen: Cluster and virial expansions for the multi-species Tonks gas
11:15–12:00 Elena Pulvirenti: Cluster expansion in the canonical ensemble: finite volume corrections and correlations

13:30–14:15 Roman Kotecký: TBA
14:30–15:15 Aldo Procacci: Some remarks on two papers by A. G. Basuev
15:30–16:15 Dimitrios Tsagkarogiannis: Free energy calculations for multi-species systems
16:30–17:15 Daniel Ueltschi: Graphical representations for quantum spin systems

Friday 3

09:30–10:15 Tim Hulshof: A lace expansion for percolation along the backbone pivotal edges
10:30–11:15 Christoph Hofer-Temmel: Cluster expansion versus disagreement percolation for hard spheres
11:30–12:15 Aernout van Enter: Use of uniqueness methods in the nonuniqueness regime

14:00–14:45 Stein Bethuelsen: Dobrushin Uniqueness Criteria
15:00–15:45 Tyler Helmuth: Loop Weighted Walk
16:00–16:45 Final discussion

Last update: June 16, 2015