Family 228Probability and statistical mechanicsLeanNot yet digested
Continuum phase transitions for radial pair potentials
Constructs stable distance-dependent pair interactions for three-dimensional classical particles with a first-order phase transition: the canonical free energy has a derivative jump at one inverse temperature throughout an open density interval. One potential has a divergent repulsive core; another is bounded and continuous with an integrable power-law tail, realizing the type of transition sought in Simon's continuum problem.
Manuscripts in this family · 2
A continuum temperature singularity for a radial pair potential
Sep 24, 2026·paper.pdfLean
We construct a stable radial pair potential in three dimensions whose canonical free energy has a strict downward derivative jump at one common finite positive inverse temperature throughout an open interval of positive densities. The potential has a divergent repulsive core, a nontrivial attractive interval, and an integrable tail satisfying . Its free-cube canonical free energy is finite at every positive inverse temperature and density.
A radial continuum phase transition with algebraic decay
Sep 24, 2026·paper.pdfLean
We construct a bounded, continuous, stable radial pair potential in three dimensions with for r ≥ 1. Throughout an open interval of positive densities, its canonical thermodynamic free energy is finite at every positive inverse temperature and has a strict downward derivative jump at one common finite positive inverse temperature.