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Updated: Jun 18, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Critical exponents from cluster coefficients.

Z Rotman¹, E Eisenberg

¹Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel. rotmanz@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

This study extends methods for calculating critical exponents in repulsive interaction models by using renormalization group arguments. A new formula accurately predicts critical behavior beyond standard limitations, validated across physical models.

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Spatial Separation of Molecular Conformers and Clusters

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Last Updated: Jun 18, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Statistical Mechanics
Thermodynamics
Condensed Matter Physics

Background:

Mayer cluster integrals for repulsive interactions transform into a matrix R_{mn}.
Standard methods fail to detect critical points due to nonphysical singularities.
Previous work linked critical exponents to a specific R matrix element decay rate (1/n^2).

Purpose of the Study:

Extend exact critical exponent calculation to more general R matrix element asymptotic behaviors.
Develop a corrected exact formula for critical exponents.
Analyze the validity and application of the new formula.

Main Methods:

Renormalization group (RG) arguments to identify asymptotic correction terms.
Analysis of general forms for R matrix element convergence.
Numerical validation of the derived formula.

Main Results:

Identified relevant asymptotic correction terms using RG.
Developed a corrected exact formula for critical exponents applicable to more general cases.
Demonstrated a physical model outside the formula's validity range.

Conclusions:

The new formula extends the exact calculation of critical exponents beyond specific decay laws.
The study provides a validated method for analyzing critical phenomena in diverse physical models.
Understanding the limits of applicability is crucial for accurate theoretical predictions.