Solution to the key problem of statistical physics -- calculations of partition function of many-body systems

Abstract

The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic systems. Here we present a novel approach that works at least four orders faster than state-of-the-art algorithms to the problem and can be applied to predict thermal properties of large molecules or macroscopic condensed matters via ab initio calculations. The method was demonstrated by C60 molecules, solid and liquid copper (up to ∼ 600GPa), solid argon, graphene and silicene on substrate, and the derived internal energy or pressure is in a good agreement with the results of vast molecular dynamics simulations in a temperature range up to 2500K, achieving a precision at least one order higher than previous methods. And, for the first time, the realistic isochoric equation of state for solid argon was reproduced directly from the partition function. II. DIRECT INTEGRAL APPROACH TO PARTITION FUNCTIONThe original sense of one-fold (1D) integral I 1D = a1 0 f (x)dx is interpreted as the sum of infinite number of rectangles with area A i = f (x i )∆x, and I 1D =

Comparison of Two Efficient Methods for Calculating Partition Functions

“…Very recently, we put forward a direct integral approach (DIA) to calculate the PF of condensed matters [25] and the high accuracy has been proved by molecular dynamics (MD) simulations of condensed copper and argon [25], graphene and γ-graphyne materials [26], and silicene [27]. Based on our reinterpreting the original sense of integral, it was shown that DIA works at least four-order faster than NS [25]. On the other hand, it has not yet been confirmed whether the DIA has improved the computational precision of precedent MC methods.…”