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Daniel Ueltschi
Daniel Ueltschi
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An impressive result of the method of cluster expansion is to derive the van der Waals equation of state for gases. Indeed, two-body interactions give the corrections to the ideal gas law. So it can be used for practical calculations!

But as Abdelmalek has remarked, the method is often used in mathematical physics to prove results. Connections with combinatorics have also been pointed recently, including the related viral expansion.

Below are some recent references; the list is not exhaustive! Notice that the method is well explained in the recent book of Friedli and Velenik (Statistical mechanics of lattice systems. A concrete mathematical introduction. Cambridge University Press, Cambridge, 2018. xix+622 pp. ISBN: 978-1-107-18482-4).

Nguyen, Tong Xuan; Fernández, Roberto Convergence of cluster and virial expansions for repulsive classical gases. J. Stat. Phys. 179 (2020), no. 2, 448–484.

Jansen, Sabine; Tsagkarogiannis, Dimitrios Cluster expansions with renormalized activities and applications to colloids. Ann. Henri Poincaré 21 (2020), no. 1, 45–79.

Jansen, S. Cluster expansions for Gibbs point processes. Adv. in Appl. Probab. 51 (2019), no. 4, 1129–1178.

MR3345409 Reviewed Pulvirenti, Elena; Tsagkarogiannis, Dimitrios Finite volume corrections and decay of correlations in the canonical ensemble. J. Stat. Phys. 159 (2015), no. 5, 1017–1039.

MR3223488 Reviewed Jansen, Sabine; Tate, Stephen J.; Tsagkarogiannis, Dimitrios; Ueltschi, Daniel Multispecies virial expansions. Comm. Math. Phys. 330 (2014), no. 2, 801–817.

MR3055378 Reviewed Morais, Thiago; Procacci, Aldo Continuous particles in the canonical ensemble as an abstract polymer gas. J. Stat. Phys. 151 (2013), no. 5, 830–849.

MR2684165 Reviewed Faris, William G. Combinatorics and cluster expansions. Probab. Surv. 7 (2010), 157–206.

MR2531305 Reviewed Poghosyan, Suren; Ueltschi, Daniel Abstract cluster expansion with applications to statistical mechanical systems. J. Math. Phys. 50 (2009), no. 5, 053509, 17 pp.

MR2468534 Reviewed Faris, William G. A connected graph identity and convergence of cluster expansions. J. Math. Phys. 49 (2008), no. 11, 113302, 14 pp.

MR2318850 Reviewed Fernández, Roberto; Procacci, Aldo Cluster expansion for abstract polymer models. New bounds from an old approach. Comm. Math. Phys. 274 (2007), no. 1, 123–140.

An impressive result of the method of cluster expansion is to derive the van der Waals equation of state for gases. Indeed, two-body interactions give the corrections to the ideal gas law. So it can be used for practical calculations!

But as Abdelmalek has remarked, the method is often used in mathematical physics to prove results. Connections with combinatorics have also been pointed recently, including the related viral expansion.

Below are some recent references; the list is not exhaustive! Notice that the method is well explained in the recent book of Friedli and Velenik (Statistical mechanics of lattice systems. A concrete mathematical introduction. Cambridge University Press, Cambridge, 2018. xix+622 pp. ISBN: 978-1-107-18482-4).

Nguyen, Tong Xuan; Fernández, Roberto Convergence of cluster and virial expansions for repulsive classical gases. J. Stat. Phys. 179 (2020), no. 2, 448–484.

Jansen, Sabine; Tsagkarogiannis, Dimitrios Cluster expansions with renormalized activities and applications to colloids. Ann. Henri Poincaré 21 (2020), no. 1, 45–79.

Jansen, S. Cluster expansions for Gibbs point processes. Adv. in Appl. Probab. 51 (2019), no. 4, 1129–1178.

MR3345409 Reviewed Pulvirenti, Elena; Tsagkarogiannis, Dimitrios Finite volume corrections and decay of correlations in the canonical ensemble. J. Stat. Phys. 159 (2015), no. 5, 1017–1039.

MR3223488 Reviewed Jansen, Sabine; Tate, Stephen J.; Tsagkarogiannis, Dimitrios; Ueltschi, Daniel Multispecies virial expansions. Comm. Math. Phys. 330 (2014), no. 2, 801–817.

MR3055378 Reviewed Morais, Thiago; Procacci, Aldo Continuous particles in the canonical ensemble as an abstract polymer gas. J. Stat. Phys. 151 (2013), no. 5, 830–849.

MR2684165 Reviewed Faris, William G. Combinatorics and cluster expansions. Probab. Surv. 7 (2010), 157–206.

MR2531305 Reviewed Poghosyan, Suren; Ueltschi, Daniel Abstract cluster expansion with applications to statistical mechanical systems. J. Math. Phys. 50 (2009), no. 5, 053509, 17 pp.

MR2468534 Reviewed Faris, William G. A connected graph identity and convergence of cluster expansions. J. Math. Phys. 49 (2008), no. 11, 113302, 14 pp.

MR2318850 Reviewed Fernández, Roberto; Procacci, Aldo Cluster expansion for abstract polymer models. New bounds from an old approach. Comm. Math. Phys. 274 (2007), no. 1, 123–140.

An impressive result of the method of cluster expansion is to derive the van der Waals equation of state for gases. Indeed, two-body interactions give the corrections to the ideal gas law. So it can be used for practical calculations!

But as Abdelmalek has remarked, the method is often used in mathematical physics to prove results. Connections with combinatorics have also been pointed recently, including the related viral expansion.

Below are some recent references; the list is not exhaustive! Notice that the method is well explained in the recent book of Friedli and Velenik (Statistical mechanics of lattice systems. A concrete mathematical introduction. Cambridge University Press, Cambridge, 2018. xix+622 pp. ISBN: 978-1-107-18482-4).

Nguyen, Tong Xuan; Fernández, Roberto Convergence of cluster and virial expansions for repulsive classical gases. J. Stat. Phys. 179 (2020), no. 2, 448–484.

Jansen, Sabine; Tsagkarogiannis, Dimitrios Cluster expansions with renormalized activities and applications to colloids. Ann. Henri Poincaré 21 (2020), no. 1, 45–79.

Jansen, S. Cluster expansions for Gibbs point processes. Adv. in Appl. Probab. 51 (2019), no. 4, 1129–1178.

Pulvirenti, Elena; Tsagkarogiannis, Dimitrios Finite volume corrections and decay of correlations in the canonical ensemble. J. Stat. Phys. 159 (2015), no. 5, 1017–1039.

Jansen, Sabine; Tate, Stephen J.; Tsagkarogiannis, Dimitrios; Ueltschi, Daniel Multispecies virial expansions. Comm. Math. Phys. 330 (2014), no. 2, 801–817.

Morais, Thiago; Procacci, Aldo Continuous particles in the canonical ensemble as an abstract polymer gas. J. Stat. Phys. 151 (2013), no. 5, 830–849.

Faris, William G. Combinatorics and cluster expansions. Probab. Surv. 7 (2010), 157–206.

Poghosyan, Suren; Ueltschi, Daniel Abstract cluster expansion with applications to statistical mechanical systems. J. Math. Phys. 50 (2009), no. 5, 053509, 17 pp.

Faris, William G. A connected graph identity and convergence of cluster expansions. J. Math. Phys. 49 (2008), no. 11, 113302, 14 pp.

Fernández, Roberto; Procacci, Aldo Cluster expansion for abstract polymer models. New bounds from an old approach. Comm. Math. Phys. 274 (2007), no. 1, 123–140.

Source Link
Daniel Ueltschi
Daniel Ueltschi
  • 66
  • 2

An impressive result of the method of cluster expansion is to derive the van der Waals equation of state for gases. Indeed, two-body interactions give the corrections to the ideal gas law. So it can be used for practical calculations!

But as Abdelmalek has remarked, the method is often used in mathematical physics to prove results. Connections with combinatorics have also been pointed recently, including the related viral expansion.

Below are some recent references; the list is not exhaustive! Notice that the method is well explained in the recent book of Friedli and Velenik (Statistical mechanics of lattice systems. A concrete mathematical introduction. Cambridge University Press, Cambridge, 2018. xix+622 pp. ISBN: 978-1-107-18482-4).

Nguyen, Tong Xuan; Fernández, Roberto Convergence of cluster and virial expansions for repulsive classical gases. J. Stat. Phys. 179 (2020), no. 2, 448–484.

Jansen, Sabine; Tsagkarogiannis, Dimitrios Cluster expansions with renormalized activities and applications to colloids. Ann. Henri Poincaré 21 (2020), no. 1, 45–79.

Jansen, S. Cluster expansions for Gibbs point processes. Adv. in Appl. Probab. 51 (2019), no. 4, 1129–1178.

MR3345409 Reviewed Pulvirenti, Elena; Tsagkarogiannis, Dimitrios Finite volume corrections and decay of correlations in the canonical ensemble. J. Stat. Phys. 159 (2015), no. 5, 1017–1039.

MR3223488 Reviewed Jansen, Sabine; Tate, Stephen J.; Tsagkarogiannis, Dimitrios; Ueltschi, Daniel Multispecies virial expansions. Comm. Math. Phys. 330 (2014), no. 2, 801–817.

MR3055378 Reviewed Morais, Thiago; Procacci, Aldo Continuous particles in the canonical ensemble as an abstract polymer gas. J. Stat. Phys. 151 (2013), no. 5, 830–849.

MR2684165 Reviewed Faris, William G. Combinatorics and cluster expansions. Probab. Surv. 7 (2010), 157–206.

MR2531305 Reviewed Poghosyan, Suren; Ueltschi, Daniel Abstract cluster expansion with applications to statistical mechanical systems. J. Math. Phys. 50 (2009), no. 5, 053509, 17 pp.

MR2468534 Reviewed Faris, William G. A connected graph identity and convergence of cluster expansions. J. Math. Phys. 49 (2008), no. 11, 113302, 14 pp.

MR2318850 Reviewed Fernández, Roberto; Procacci, Aldo Cluster expansion for abstract polymer models. New bounds from an old approach. Comm. Math. Phys. 274 (2007), no. 1, 123–140.