Non-classical critical exponents at Bose-Einstein condensation

Abstract

We show that ideal Bose-Einstein condensation (BEC) in $d = 3$ dimensions is a non-classical critical second order phase transition with exponents $\alpha = -1$, $\beta = 1$, $\gamma = 1$, $\delta = 2$, $\eta = 1$ and $\nu = 1$, obeying all the scaling equalities. These results are found with no approximations or assumptions. The previous exponents are a critical universality class on its own, different from the so-far accepted notion that BEC belongs to the Spherical Model universality class.