Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model

Understand

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite.

• These singularities are smoothed out at a finite temperature but leave behind non-trivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points.
• We illustrate some of these issues using the classical non-linear O(2) sigma model with a coupling $\beta$ and chemical potential $\mu$ on a 2+1 dimensional Euclidean lattice.
• In the conventional formulation this model suffers from a sign problem at non-zero chemical potential and hence cannot be studied with the Wolff cluster algorithm.