Virial Coefficients for the Hard-Core Gas in Two Dimensions

Abstract

The fourth virial coefficient for a gas of hard disks is calculated by means of the virial theorem. The exact result is $B_4{\mathrm{/b}}^3\text{=2–9}\sqrt{3}{\text{/2π+10π}}^{\text{−2}}$ , where b is the second virial coefficient. The numerical value for B₄/b³ of 0.532232 confirms previous estimates obtained by Monte Carlo integration. The weights of all four‐point irreducible clusters are also recorded.