# Finite size effects in the presence of a chemical potential: A study in the classical non-linear O2 sigma-model - High Energy Physics - Lattice

Finite size effects in the presence of a chemical potential: A study in the classical non-linear O2 sigma-model - High Energy Physics - Lattice - Download this document for free, or read online. Document in PDF available to download.

Abstract: In the presence of a chemical potential, the physics of level crossings leadsto singularities at zero temperature, even when the spatial volume is finite.These singularities are smoothed out at a finite temperature but leave behindnon-trivial finite size effects which must be understood in order to extractthermodynamic quantities using Monte Carlo methods, particularly close tocritical points. We illustrate some of these issues using the classicalnon-linear O2 sigma model with a coupling $\beta$ and chemical potential$\mu$ on a 2+1 dimensional Euclidean lattice. In the conventional formulationthis model suffers from a sign problem at non-zero chemical potential and hencecannot be studied with the Wolff cluster algorithm. However, when formulated interms of world-line of particles, the sign problem is absent and the model canbe studied efficiently with the -worm algorithm-. Using this method we studythe finite size effects that arise due to the chemical potential and develop aneffective quantum mechanical approach to capture the effects. As a side resultwe obtain energy levels of up to four particles as a function of the box sizeand uncover a part of the phase diagram in the $\beta,\mu$ plane.

Author: ** Debasish Banerjee, Shailesh Chandrasekharan**

Source: https://arxiv.org/