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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 β and chemical
potential μ on a 2+1-dimensional 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 (β,μ) plane. © 2010 The American Physical Society.
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Journal articlePermalink
https://hdl.handle.net/10161/4275Published Version (Please cite this version)
10.1103/PhysRevD.81.125007Publication Info
Banerjee, D; & Chandrasekharan, S (2010). Finite size effects in the presence of a chemical potential: A study in the classical
nonlinear O(2) sigma model. Physical Review D - Particles, Fields, Gravitation and Cosmology, 81(12). pp. 125007. 10.1103/PhysRevD.81.125007. Retrieved from https://hdl.handle.net/10161/4275.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Shailesh Chandrasekharan
Professor of Physics
Prof. Chandrasekharan is interested in understanding quantum field theories non-perturbatively
from first principles calculations. His research focuses on lattice formulations of
these theories with emphasis on strongly correlated fermionic systems of interest
in condensed matter, particle and nuclear physics. He develops novel Monte-Carlo algorithms
to study these problems. He is particularly excited about solutions to the notoriously
difficult <a href="http://en.wikipedia.org/wiki/Numerical_si

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