Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model
Abstract
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 nontrivial 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 nonlinear O(2) sigma model with a coupling {beta} and chemical potential {mu} on a 2+1dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the 'worm algorithm'. Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the ({beta},{mu}) plane.
 Authors:

 Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005 (India)
 Publication Date:
 OSTI Identifier:
 21408103
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 81; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.81.125007; (c) 2010 The American Physical Society; Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; CAPTURE; COMPUTERIZED SIMULATION; COUPLING; ENERGY LEVELS; EUCLIDEAN SPACE; MONTE CARLO METHOD; NONLINEAR PROBLEMS; ONEDIMENSIONAL CALCULATIONS; PHASE DIAGRAMS; QUANTUM MECHANICS; SIGMA MODEL; SINGULARITY; BOSONEXCHANGE MODELS; CALCULATION METHODS; DIAGRAMS; INFORMATION; MATHEMATICAL LOGIC; MATHEMATICAL MODELS; MATHEMATICAL SPACE; MECHANICS; PARTICLE MODELS; PERIPHERAL MODELS; RIEMANN SPACE; SIMULATION; SPACE
Citation Formats
Banerjee, Debasish, Chandrasekharan, Shailesh, and Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708. Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVD.81.125007.
Banerjee, Debasish, Chandrasekharan, Shailesh, & Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708. Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model. United States. doi:10.1103/PHYSREVD.81.125007.
Banerjee, Debasish, Chandrasekharan, Shailesh, and Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708. Tue .
"Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model". United States. doi:10.1103/PHYSREVD.81.125007.
@article{osti_21408103,
title = {Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model},
author = {Banerjee, Debasish and Chandrasekharan, Shailesh and Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708},
abstractNote = {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 nontrivial 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 nonlinear O(2) sigma model with a coupling {beta} and chemical potential {mu} on a 2+1dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the 'worm algorithm'. Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the ({beta},{mu}) plane.},
doi = {10.1103/PHYSREVD.81.125007},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 12,
volume = 81,
place = {United States},
year = {2010},
month = {6}
}