This title appears in the Scientific Report :
2018
Expanding the effective action around non-Gaussian theories
Expanding the effective action around non-Gaussian theories
The effective action or Gibbs Free Energy is the central quantity to study phase transitions and is at the core of effective theories constructed, for example, by the renormalization group. It is known that only one-line-irreducible Feynman diagrams contribute in the case that the theory, about whic...
| Personal Name(s): | Kühn, Tobias (Corresponding author) |
|---|---|
| Helias, Moritz | |
| Contributing Institute: |
Computational and Systems Neuroscience; INM-6 Jara-Institut Brain structure-function relationships; INM-10 Computational and Systems Neuroscience; IAS-6 |
| Imprint: |
2018
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| Conference: | DPG Spring Meeting, Section Condensed Matter, Berlin (Germany), 2018-03-11 - 2018-03-16 |
| Document Type: |
Conference Presentation |
| Research Program: |
Theory of multi-scale neuronal networks Supercomputing and Modelling for the Human Brain Human Brain Project Specific Grant Agreement 1 Connectivity and Activity Theory, modelling and simulation |
| Publikationsportal JuSER |
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The effective action or Gibbs Free Energy is the central quantity to study phase transitions and is at the core of effective theories constructed, for example, by the renormalization group. It is known that only one-line-irreducible Feynman diagrams contribute in the case that the theory, about which one expands, is Gaussian. We introduce a generalized notion of one-line-irreducibility: diagrams that remain connected after detaching a single leg of an interaction vertex. We show that the effective action decomposes into diagrams that are either irreducible in this more general sense or belong to a second class of diagrams that has no analogue in Gaussian theories [Kühn & Helias 2017, arXiv:1711.05599]. The presented method allows the efficient diagrammatic perturbative computation of the effective action around any exactly solvable problem. We illustrate this method by application to the (classical) Ising model expanded in the coupling strength. This reproduces the Plefka expansion [Plefka 1982], including the TAP-correction [Thouless et al. 1977] to mean-field theory. We find that the diagrammatic formulation considerably simplifies the calculation compared to existing techniques [Takayama & Nakanishi 1997, Georges & Yedidia 1991]. Supported by the Helmholtz foundation (VH-NG-1028, SMHB); EU Grant 604102 (HBP). |