Efficient approaches to solutions of partition function for condensed matters

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Computational Chemistry

Background:

• Accurately calculating the partition function (or free energy) remains a century-old challenge in statistical physics.
• This hinders the predictive power of statistical mechanics for condensed matter thermodynamic properties.
• Existing methods lack the required efficiency and precision for complex systems.

Purpose of the Study:

• To address the limitations of the Direct Integral Approach (DIA).
• To develop a new method to overcome DIA's shortcomings for low-density condensed systems.
• To enhance the computational efficiency and precision in calculating thermodynamic properties.

Main Methods:

• Developed and examined the Direct Integral Approach (DIA).
• Established a novel method to complement DIA for lower-density systems.
• Validated methods using empirical potentials for copper, argon, and C60 molecules.
• Compared results with extensive molecular dynamics simulations.

Main Results:

• Achieved ultrahigh computational efficiency and precision, approximately ten times higher than previous methods.
• Successfully reproduced the experimental equation of state for solid copper up to ~600 GPa.
• Demonstrated accuracy up to the melting point for various condensed systems.
• Enabled ab initio calculations due to ultrahigh efficiency.

Conclusions:

• The developed methods significantly advance the calculation of partition functions for condensed matter.
• These methods offer unprecedented accuracy and efficiency, enabling predictions from first principles.
• The findings pave the way for more accurate theoretical predictions of material properties.