Thermal Transitions Reveal Singularities And Changes In Quantum Systems

Shaun D. Hampton and colleagues at the Korea Institute for Advanced Study compute the perturbative expansion of thermal free energy to high orders, extracting key data that characterise the transition between the bounce and the sphaleron, critical phenomena in quantum mechanics involving metastable vacuum decay. The calculations determine the transition temperature and order, alongside the decay rate, including the one-loop prefactor, solely from perturbative calculations, avoiding the need for semiclassical approximations. The findings reveal how the behaviour of Borel singularities reflects the nature of the transition, smoothly joining for second-order transitions and exhibiting a distinct kink for first-order ones.