Partition Function of the Model of Perfect Gas of Clusters for Interacting Fluids

Siudem, Grzegorz

doi:10.1016/s0034-4877(14)60006-9

Cited by 8 publications

(12 citation statements)

References 7 publications

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“…The non-negative character of these coefficients is very significant: It brings to mind the so-called perfect gas of clusters model 30 , in which the coefficients, i.e. { a n }, stand for the number of microscopic realisations of clusters of size n 25 31 32 33 . For completeness, let us recall that in the perfect gas of clusters model, particles constituting a fluid may interact only when they belong to the same cluster (i.e.…”

Section: Discussionmentioning

confidence: 99%

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

Siudem

Fronczak

2016

Sci Rep

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In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

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Section: Discussionmentioning

confidence: 99%

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

Siudem

Fronczak

2016

Sci Rep

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“…Next, we present the essential in our work Bell polynomials' approach introduced in [22]. As an example, summarizing our previous work [49], we consider the square lattice Ising model, in which we obtained the exact formulas for the number of states as well as combinatorial interpretation in the terms of the ideal gas of clusters [20,21,48]. We also present the generalization of the square, triangular and hexagonal lattices -Utiyama chequered graphs [52], which are considered later in the paper.…”

Section: Tools and Methodsmentioning

confidence: 99%

“…(5,6,7). Furthermore, this technique allows to reinterpret the considered lattice models as a gas of clusters models [20,21,48]. As an illustration of the Bell polynomials' approach, we consider two-dimensional square lattice and encapsulate our previous work [49].…”

Section: Bell Polynomials' Approachmentioning

confidence: 99%

“…As long as free-energy coefficients a (n) are non-negative (compare Example 1) one could see [22] in the Bell polynomials in Eq. ( 40) partition function of the corresponding perfect gas of clusters model [20,21,48]. This model is a generalization of the ideal gas concept, where particles interact only within the same cluster.…”

Section: Perfect Gas Of Clustersmentioning

confidence: 99%

“…They were widely applied, in particular, in the case of the lattice models (see sec. II in [39] and [5,17,20,21,22,24,48,49,53,56]). In this work we concentrate mainly on the lowtemperature expansion and its dual (in sense of Kramers-Wannier) counterpart i.e.…”

Section: Introductionmentioning

confidence: 97%

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Bell polynomials in the series expansions of the Ising model

Siudem,

Fronczak

2020

Preprint

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Through applying Bell polynomials to the integral representation of the free energy of the Ising model for the triangular and hexagonal lattices we obtain the exact combinatorial formulas for the number of spin configurations at a given energy (i.e. low-temperature series expansion of the partition function or, alternatively, the number of states). We also generalize this approach to the wider class of the (chequered) Utiyama graphs. Apart from the presented exact formulas, our technique allows one to establish the correspondence between the perfect gas of clusters and the Ising model on the lattices which have positive coefficients in the low-temperature expansion (e.g. square lattice, hexagonal lattice). However it is not always the case -we present that for the triangular lattice the coefficients could be negative and the perfect gas of clusters interpretation is problematic.

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Energy spectrum of interacting gas: Cluster expansion method

Chen

et al. 2022

Chemical Physics

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Partition Function of the Model of Perfect Gas of Clusters for Interacting Fluids

Cited by 8 publications

References 7 publications

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

Bell polynomials in the series expansions of the Ising model

Energy spectrum of interacting gas: Cluster expansion method

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