- Field-theoretic simulation
A

**field-theoretic simulation**is a numerical strategy to calculate structure and physical properties of a many-particle system within the framework of astatistical field theory , like e.g. apolymer field theory . A convenient possibility is to useMonte Carlo (MC) algorithms, to sample the full partition function integral expressed in field-theoretic representation. The procedure is then called theauxiliary field Monte Carlo method. However, it is well-known that MC sampling in conjunction with the basic field-theoretic representation of the partition function integral, directly obtained via theHubbard Stratonovich transformation , is impracticable, due to the so-callednumerical sign problem (Baeurle 2002, Fredrickson 2002). The difficulty is related to the complex and oscillatory nature of the resulting distribution function, which causes a bad statistical convergence of the ensemble averages of the desired structural and thermodynamic quantities. In such cases special analytical and numerical techniques are required to accelerate the statistical convergence of the field-theoretic simulation (Baeurle 2003, Baeurle 2003a, Baeurle 2004).**Shifted-contour Monte Carlo technique****Mean field representation**To make the field-theoretic methodology amenable for computation, Baeurle proposed to shiftthe contour of integration of the partition function integral through the homogeneous mean field (MF) solution using

Cauchy's integral theorem , which provides its so-called "mean-field representation". This strategy was previously successfully employed in field-theoretic electronic structure calculations (Rom 1997, Baer 1998). Baeurle could demonstrate that this technique provides a significant acceleration of the statistical convergence of the ensemble averages in the MC sampling procedure (Baeurle 2002).**Gaussian equivalent representation**In subsequent works Baeurle et al. (Baeurle 2002, Baeurle 2002a) applied the concept of tadpole renormalization, which originates from

quantum field theory and leads to the "Gaussian equivalent representation" of the partition function integral, in conjunction with advanced MC techniques in the grand canonical ensemble. They could convincingly demonstrate that this strategy provides an additional boost in the statistical convergence of the desired ensemble averages (Baeurle 2002).**Alternative techniques**Other promising field-theoretic simulation techniques have been developed recently, but they either still lack the proof of correct statistical convergence, like e.g. the Complex Langevinmethod (Ganesan 2001), and/or still need to prove their effectiveness on systems, where multiple saddle points are important (Moreira 2003).

**References*** cite journal |

url = http://prola.aps.org/abstract/PRL/v89/i8/e080602

last = Baeurle

first = S.A.

title = Method of Gaussian Equivalent Representation: A New Technique for Reducing the Sign Problem of Functional Integral Methods

journal = Phys. Rev. Lett.

volume = 89

pages = 080602

year = 2002* cite journal

url = http://www.mrl.ucsb.edu/~ghf/ghfgroup/pubs/pub156.pdf

last = Fredrickson

first = G.H.

coauthors = Ganesan, V.; Drolet, F.

title = Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids

journal = Macromolecules

volume = 35

pages = 16

year = 2002* cite journal

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHY-47MKK8M-2&_user=616165&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=60e4b8712970cf7e07a14b05c5f0e609

last = Baeurle

first = S.A.

title = Computation within the auxiliary field approach

journal = J. Comput. Phys.

volume = 184

pages = 540

year = 2003* cite journal |

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-48XCNNY-3&_user=616165&_coverDate=08%2F01%2F2003&_alid=745709877&_rdoc=6&_fmt=high&_orig=search&_cdi=5301&_sort=d&_docanchor=&view=c&_ct=8&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=c5a0e9b03b74325c0dc7bf7d88406ecf

last = Baeurle

first = S.A.

title = The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies

journal = Comput. Phys. Commun.

volume = 154

pages = 111

year = 2003a* cite journal |

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ5-4BHK1JN-4&_user=616165&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=fe7a7f52aadb5375994112ee03cebefc

last = Baeurle

first = S.A.

title = Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density

journal = Comput. Phys. Commun.

volume = 157

pages = 201

year = 2004* cite journal |

url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TFN-3S9T08S-1K&_user=616165&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000032338&_version=1&_urlVersion=0&_userid=616165&md5=afcc30c50e0dd059360e1eb6c9feb448

last = Rom

first = N.

coauthors = Charutz, D.M.; Neuhauser, D.

title = Shifted-contour auxiliary-field Monte Carlo: circumventing the sign difficulty for electronic-structure calculations

journal = Chem. Phys. Lett.

volume = 270

pages = 382

year = 1997* cite journal |

url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000109000015006219000001&idtype=cvips&gifs=yes

last = Baer

first = R.

coauthors = Head-Gordon, M.; Neuhauser, D.

title = Shifted-contour auxiliary field Monte Carlo for ab initio electronic structure: Straddling the sign problem

journal = J. Chem. Phys.

volume = 109

pages = 6219

year = 1998* cite journal

url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000117000007003027000001&idtype=cvips&gifs=yes

last = Baeurle

first = S.A.

coauthors = Martonak, R.; Parrinello, M.

title = A field-theoretical approach to simulation in the classical canonical and grand canonical ensemble

journal = J. Chem. Phys.

volume = 117

pages = 3027

year = 2002a* cite journal

url = http://www.iop.org/EJ/article/0295-5075/55/6/814/epl_55_6_814.pdf?request-id=dfd06fed-53f4-41e8-9835-09aa202962d5

last Ganesan

first = V.

coauthors = Fredrickson, G.H.

title = Field-theoretic polymer simulations

journal = Europhys. Lett.

volume = 55

pages = 814

year = 2001* cite journal

url = http://prola.aps.org/abstract/PRL/v91/i15/e150201

last Moreira

first = A.G.

coauthors = Baeurle, S.A.; Fredrickson, G.H.

title = Global Stationary Phase and the Sign Problem

journal = Phys. Rev. Lett.

volume = 91

pages = 150201

year = 2003**External Links*** [

*http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/index.html Particle and Polymer Field Theories*]

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