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The Theory of Critical Phenomena: An Introduction to the Renormalization Group
Abstract
The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.
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“whereas 2D tensor-network methods (PEPS, MERA) in principle work for arbitrarily big systems (bosonic, and even fermionic [83] or frustrated [84]) but are biased towards slightly entangled states.”
From Can one trust quantum simulators? (2012) · cites this paper as [83]
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Self-citation
Metadata
- Authors
- Binney, J. J., Dowrick, N. J., Fisher, A. J., & Newman, M. E. J.
- Affiliations
- University of Oxford (GB)
- Cornell University (US)
- Publisher
- Oxford University PressOxford
- Published
- 1992-06-11
- OpenAlex
- W1558680194
- Cited by
- 1,243
- References
- 0
- Citations by year
- 2026: 17 · 2025: 42 · 2024: 22 · 2023: 24 · 2022: 25 · 2021: 32 · 2020: 25 · 2019: 57 · 2018: 27 · 2017: 32 · 2016: 32 · 2015: 35 · 2014: 42 · 2013: 46 · 2012: 42
- FWCI
- 3.84
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- UCL Discovery (University College London) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- critical phenomena, critical exponents, second-order phase transition, scaling theory, field theory, real-space renormalization group, mean-field theory, Landau-Ginzburg models, diagrammatic perturbation theory, exact solutions, numerical simulation, statistical mechanics
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