Extended Mean Field study of complex $\phi^4$-theory at finite density and temperature

TL;DR

This paper applies Extended Mean Field Theory to complex scalar $\

Contribution

It demonstrates that EMFT accurately reproduces critical phenomena and phase diagrams of complex $\

Findings

EMFT results agree well with Monte Carlo data across parameter space.

EMFT captures Silver Blaze phenomenon at zero temperature.

EMFT enables study of lattice spacings inaccessible to Monte Carlo.

Abstract

We review the Extended Mean Field Theory (EMFT) approximation and apply it to complex, scalar $\phi^4$-theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $\mu$ at both zero and nonzero temperature and determine the $(T,\mu)$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the "Silver Blaze" behavior at zero temperature and dimensional reduction at finite temperature.