
Published online:
23 March 2023
Published in print:
28 February 2023
Online ISBN:
9780191939778
Print ISBN:
9780192847485
Contents
-
-
-
-
-
-
-
-
5.1 Mean-field solutions 5.1 Mean-field solutions
-
5.1.1 Root-finding versus optimization 5.1.1 Root-finding versus optimization
-
5.1.2 Auxiliary field polymer models 5.1.2 Auxiliary field polymer models
-
5.1.3 Coherent state polymer models 5.1.3 Coherent state polymer models
-
5.1.4 Coherent state boson models 5.1.4 Coherent state boson models
-
-
5.2 Including fluctuations: field-theoretic simulations 5.2 Including fluctuations: field-theoretic simulations
-
5.2.1 Models without a sign problem 5.2.1 Models without a sign problem
-
5.2.2 Complex Langevin theory 5.2.2 Complex Langevin theory
-
5.2.3 Algorithms for AF polymer models 5.2.3 Algorithms for AF polymer models
-
5.2.4 Algorithms for CS polymer models 5.2.4 Algorithms for CS polymer models
-
5.2.5 Algorithms for CS boson models 5.2.5 Algorithms for CS boson models
-
Inclusion of gauge fields Inclusion of gauge fields
-
Quantum lattice models Quantum lattice models
-
Quantum spin models Quantum spin models
-
Bose fluid in the canonical ensemble Bose fluid in the canonical ensemble
-
Higher-order imaginary-time accuracy Higher-order imaginary-time accuracy
-
-
-
5.3 Methodology, error analysis, and troubleshooting 5.3 Methodology, error analysis, and troubleshooting
-
5.3.1 Mean-field solutions 5.3.1 Mean-field solutions
-
Resolution Resolution
-
Stopping criterion Stopping criterion
-
Initial condition Initial condition
-
Roundoff errors Roundoff errors
-
Underflow or overflow Underflow or overflow
-
-
5.3.2 Field-theoretic simulations 5.3.2 Field-theoretic simulations
-
Time-step errors in fictitious time Time-step errors in fictitious time
-
Random number bias Random number bias
-
Statistical sampling errors Statistical sampling errors
-
Failure of complex Langevin sampling Failure of complex Langevin sampling
-
-
5.3.3 Troubleshooting 5.3.3 Troubleshooting
-
-
-
-
-
-
Chapter
5 Numerical Methods for Field-Theoretic Simulations
Get access
Pages
149–229
-
Published:February 2023
Cite
Delaney, Fredrickson, and Kris T. Delaney, 'Numerical Methods for Field-Theoretic Simulations', Field-Theoretic Simulations in Soft Matter and Quantum Fluids (Oxford , 2023; online edn, Oxford Academic, 23 Mar. 2023), https://doi.org/10.1093/oso/9780192847485.003.0005, accessed 13 May 2025.
Abstract
Chapter 5 provides an introduction to the numerical methods used to obtain mean-field solutions and conduct field-theoretic simulations of the field theory models developed in Chapters 2 and 3. The chapter discusses algorithms that exploit efficient FFT-based field operations and balance stability and accuracy. Mean-field solutions are obtained by deterministic relaxation, while the sign problem inherent to classical and quantum field theories mandates the use of complex Langevin sampling methods in stochastic field-theoretic simulations. Practical guidelines for conducting simulations, assessing errors, and troubleshooting are provided.
Fredrickson Delaney, Oxford University Press. © Delaney (2023). DOI: 10.1093/oso/9780192847485.003.0005
You do not currently have access to this chapter.
Sign in
Personal account
- Sign in with email/username & password
- Get email alerts
- Save searches
- Purchase content
- Activate your purchase/trial code
- Add your ORCID iD
Purchase
Our books are available by subscription or purchase to libraries and institutions.
Purchasing informationMetrics
View Metrics
Metrics
Total Views
27
20
Pageviews
7
PDF Downloads
Since 4/1/2023
Month: | Total Views: |
---|---|
April 2023 | 6 |
October 2023 | 1 |
November 2023 | 1 |
December 2023 | 2 |
April 2024 | 2 |
May 2024 | 3 |
June 2024 | 2 |
July 2024 | 1 |
August 2024 | 3 |
November 2024 | 1 |
December 2024 | 3 |
March 2025 | 2 |
Citations
More from Oxford Academic
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.