Hard-core exclusion retained at zero inverse temperature

In the dimensionless coordinates of Stable regularly tempered classical positional preparation, take $d=1$, an interval $\mathrm{\Lambda }=[0,L]$, and a hard-core exclusion distance $a$ with $0<a<L$. Both $L$ and $a$ are dimensionless; the physical interval length and exclusion distance are ${\mathrm{\ell }}_{0}L$ and ${\mathrm{\ell }}_{0}a$ in metres. Set $\phi (r)=+\mathrm{\infty }$ for $\mathrm{\mid }r\mathrm{\mid }<a$ and $0$ otherwise. Under the retained-admissibility zero-inverse-temperature preparation at $z>0$, the two-particle weight is zero on $\mathrm{\mid }{x}_1-x_2\mathrm{\mid }<a$ and equals $z^2$ on $\mathrm{\mid }{x}_1-x_2\mathrm{\mid }\ge a$. Hence the retained grand law is not the unrestricted Poisson activity law, which assigns positive mass to the forbidden two-particle band. The conclusion concerns the finite positional continuation defined on the A page.