# Continuous Particles in the Canonical Ensemble as an Abstract Polymer Gas

@article{Morais2013ContinuousPI, title={Continuous Particles in the Canonical Ensemble as an Abstract Polymer Gas}, author={Thiago Morais and Aldo Procacci}, journal={Journal of Statistical Physics}, year={2013}, volume={151}, pages={830-849} }

We revisit the expansion recently proposed by Pulvirenti and Tsagkarogiannis for a system of N continuous particles in the Canonical Ensemble. Under the sole assumption that the particles interact via a tempered and stable pair potential and are subjected to the usual free boundary conditions, we show the analyticity of the Helmholtz free energy at low densities and, using the Penrose tree graph identity, we establish a lower bound for the convergence radius which happens to be identical to the…

## 15 Citations

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The pressure of a gas of particles with a uniformly repulsive pair interaction in a finite container is shown to satisfy (exactly as a formal object) a "viscous" Hamilton-Jacobi (H-J) equation whose…

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We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds…

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- MathematicsLetters in Mathematical Physics
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We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds…

### Virial Expansion Bounds

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Mayer’s second theorem in the context of a classical gas model allows us to write the coefficients of the virial expansion of pressure in terms of weighted two-connected graphs. Labelle, Leroux and…

### Cluster Expansion for the Ising Model in the Canonical Ensemble

- MathematicsMathematical Physics, Analysis and Geometry
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We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare the lower bound of its radius of convergence with the one computed by the virial expansion…

### Virial Expansion Bounds Through Tree Partition Schemes

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The bound on the radius of convergence in the case of the Penrose partition scheme is the same as that proposed by Groeneveld and improves the bound achieved by Lebowitz and Penrose.

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