The DOI matches its Crossref record.
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
Citations
Cited by
Sorted by citations
Items 801–900 of 1,000
Resilience reconsidered: Case histories from disease ecologyPreprint
Wallace, R., & Wallace, D. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.q-bio/0310009 · Cited by 1
Non-Fractal Critical Clusters at the Percolation Transition
Yakubo, K., & Mitobe, M. (2007) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.76.034004 · Cited by 3
Connes’ spectral triple and U(1) gauge theory on finite sets
Hu, L., & Sant’Anna, A. S. (2002) · Journal of Geometry and Physics · doi:10.1016/s0393-0440(01)00093-6 · Cited by 3
Critical behavior in unconventional ferromagnetic superconductors
Uzunov, D. I. (2006) · Physical Review B · doi:10.1103/physrevb.74.134514 · Cited by 3
Heat transport and nonthermal excitations in vibrational hopping systems
Böttger, H., & Damker, T. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.12481 · Cited by 3
New magnetic effects on the phase transitions in unconventional superconductors
Uzunov, D. I. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/77/20008 · Cited by 3
Simulation of Critical Properties of EuTe on the Creutz Cellular Automaton
Gwizdałła, T. M. (2004) · Czechoslovak Journal of Physics · doi:10.1007/s10582-004-0172-6 · Cited by 3
Phenomena, Models and Understanding : The Lenz-Ising model and critical phenomena 1920-1971
Niss, M. (2005) · RUCforsk (Roskilde University) · Cited by 3
X-ray Diffraction Studies on the Effect of Additives on the Phase Behaviour of Lipids
Rapp, G., Funari, S. S., Richter, F., et al. (2001) · Springer eBooks · doi:10.1007/978-3-662-04496-4_8 · Cited by 3
Morales, G. B., Santo, S. D., & Muñoz, M. A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.11.23.469734 · Cited by 3
Physics of Jerky Motion in Slowly Driven Magnetic and Earthquake Fault Systems
Dahmen, K. A., & Ben‐Zion, Y. (2022) · Encyclopedia of complexity and systems science series · doi:10.1007/978-1-0716-1454-9_299 · Cited by 3
Chen, Q., & Prokopenko, M. (2025) · Royal Society Open Science · doi:10.1098/rsos.241655 · Cited by 2
Critical size for sustaining magnetic flux: Revisiting ∇·B = 0 at the nanoscale
Shi, D. (2025) · MRS Communications · doi:10.1557/s43579-025-00818-6 · Cited by 2
del Pino, H. V., & Cuerno, R. (2025) · Physical Review Research · doi:10.1103/y9b7-z6zq · Cited by 2
Morales, G. B., Santo, S. D., & Muñoz, M. A. (2025) · SEMA SIMAI Springer series · doi:10.1007/978-3-031-99044-1_2 · Cited by 3
Signatures of infinity: Nonergodicity and resource scaling in prediction, complexity, and learning
Crutchfield, J. P., & Marzen, S. (2015) · Physical Review E · doi:10.1103/physreve.91.050106 · Cited by 15
Gałązka, M., & Zieliński, P. (2012) · physica status solidi (b) · doi:10.1002/pssb.201147556 · Cited by 2
Transition from compact to porous films in deposition with temperature-activated diffusion
di Caprio, D., & Reis, F. D. A. A. (2015) · Physical Review E · doi:10.1103/physreve.92.012402 · Cited by 2
Analysis of the IR-Raman Modes and the Heat Capacity Near the α-Inc-β Transitions in Quartz
Yurtseven, H., Günay, E., Karacali, H., et al. (2021) · Ferroelectrics · doi:10.1080/00150193.2021.1916356 · Cited by 2
Pan, J.-S. (2022) · Physical Review A · doi:10.1103/physreva.105.013306 · Cited by 2
Więckowski, J., Szewczyk, A., Gutowska, M. U., et al. (2025) · Physical review. B./Physical review. B · doi:10.1103/hn32-kxms · Cited by 2
Unsupervised detection of semantic correlations in big data
Acevedo, S., Rodríguez, Á., & Laio, A. (2025) · Communications Physics · doi:10.1038/s42005-025-02115-z · Cited by 4
Modeling Disinformation Spread in Social Networks: Phase Transitions and Mean-Field Analysis
Evangelatos, S., Veroni, E., Efthymiou, V., & Nikolopoulos, C. D. (2025) · ACM Transactions on the Web · doi:10.1145/3747287 · Cited by 2
Marcenko-Pastur Distribution and McKay’s Law
Wang, C. (2013) · Springer eBooks · doi:10.1007/978-3-642-38565-0_7 · Cited by 2
Theory of Ferromagnetic Unconventional Superconductors with Spin-Triplet Electron Pairing
Dimo, I. (2012) · InTech eBooks · doi:10.5772/48579 · Cited by 2
de Vega, H. J., Sanchez, N. G., & Combes, F. (1998) · Springer eBooks · doi:10.1007/978-94-011-5046-0_22 · Cited by 2
Theoretical Tools in Modeling Communication and Language Dynamics
Loreto, V. (2009) · Springer eBooks · doi:10.1007/978-3-642-01250-1_5 · Cited by 2
Thermodynamical relations at characteristic points
Matlak, M. (2008) · Phase Transitions · doi:10.1080/01411590802031311 · Cited by 2
On the mild and wild mechanical roughness of the lithosphere
Gudehus, G. (2012) · Obras y proyectos · doi:10.4067/s0718-28132012000100005 · Cited by 2
Wang, Y.-M. (2006) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2006.01.011 · Cited by 2
Scattering of light in a ferroelectric with incommensurate phase: K2ZnCl4
Горелик, В. С., Moiseenko, V. N., & Pastukhov, V. I. (1995) · Journal of Russian Laser Research · doi:10.1007/bf02581076 · Cited by 2
Mirzaev, S. Z., & Kaatze, U. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4862825 · Cited by 2
Pisanova, E. S., & Tonchev, N. S. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/253/1/012020 · Cited by 2
Effect of random crystal field on a doubly decorated ferrimagnetic Ising model
Benayad, M. R., Benyoussef, A., & Kenz, A. E. (2011) · Phase Transitions · doi:10.1080/01411594.2010.535135 · Cited by 2
Monte Carlo simulation of point defects in BCC iron
Itakura, M., Kaburaki, H., & KUSUNOKI, K. (1999) · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms · doi:10.1016/s0168-583x(99)00205-0 · Cited by 2
Langevin vortex dynamics for a layered superconductor in the lowest-Landau-level approximation
Al-Saidi, W. A., & Stroud, D. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.144511 · Cited by 2
Solution Structure in Supercritical Fluids
Arai, Y., Sako, T., & Takebayashi, Y. (2002) · Springer eBooks · doi:10.1007/978-3-642-56238-9_1 · Cited by 2
Zhou, Y. (2014) · Physical Review A · doi:10.1103/physreva.89.052318 · Cited by 2
Gravitational and Barrier Effects in D-Dimensional Invasion Percolation Reservoir Models
Hawick, K. A. (2011) · doi:10.2316/p.2011.756-036 · Cited by 2
Gałązka, M., & Zieliński, P. (2010) · Acta Physica Polonica A · doi:10.12693/aphyspola.117.566 · Cited by 2
Accurate Critical Parameters for the Modified Lennard-Jones Model
Okamoto, K., & Fuchizaki, K. (2017) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.86.034003 · Cited by 2
Zhu, W. Q. (1999) · Advances in Structural Engineering · doi:10.1177/136943329900200302 · Cited by 2
Statistical Mechanics and Critical Phenomena: A Brief Overview
Santra, S. B., & Ray, P. (2011) · Texts and readings in physical sciences · doi:10.1007/978-93-86279-50-7_1 · Cited by 2
The KCOD Model on (3,4,6,4) and (34,6) Archimedean Lattices
Lima, F. D. S. (2017) · Entropy · doi:10.3390/e19090459 · Cited by 2
Critical Limit Principle of Maximum Entropy and Reinterpretation of Scaling Laws
Feng, Y.-G. (2018) · Journal of Modern Physics · doi:10.4236/jmp.2018.911128 · Cited by 2
Mondaini, R. P., & Neto, S. C. D. A. (2019) · Springer eBooks · doi:10.1007/978-3-030-23433-1_10 · Cited by 2
Richter, D., Monkenbusch, M., & Schwahn, D. (2012) · Elsevier eBooks · doi:10.1016/b978-0-444-53349-4.00030-3 · Cited by 2
A complex system approach to language evolution
Colaiori, F., & Tria, F. (2020) · Evolutionary Linguistic Theory · doi:10.1075/elt.00018.col · Cited by 2
Phase transitions to spin-triplet ferromagnetic superconductivity in neutron stars
Shopova, D. V., Tsvetkov, T. E., & Uzunov, D. I. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2
Saito, K., & Yamamura, Y. (2022) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.91.104603 · Cited by 2
Free Energy of Mixing for Polymer Solutions
Yamamoto, T., Narita, T., Nobe, M., et al. (2004) · Macromolecules · doi:10.1021/ma035435w · Cited by 2
Karmakar, S. K., Giri, S., & Majumdar, S. (2020) · physica status solidi (b) · doi:10.1002/pssb.202000273 · Cited by 2
General method to sample systems in the microcanonical ensemble using Monte Carlo simulations
Palma, G., & Riveros, A. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-020-00022-6 · Cited by 2
Critical Exponents, Universality Class, and Thermodynamic “Temperature” of the Brain
Yu, S. P., Yang, H., Shriki, O., & Plenz, D. (2014) · Wiley eBooks · doi:10.1002/9783527651009.ch14 · Cited by 2
Scaling of Noise and Constructive Aspects of Fluctuations
Vilar, J. M. G., & Rubı́, J. M. (2007) · Springer eBooks · doi:10.1007/3-540-45396-2_12 · Cited by 2
The Magnetic Properties of Sputtered Pd1−xMnx Films for Thermometry and Bolometry
Nelson, R. C., Sergatskov, D. A., & Duncan, R. V. (2002) · Journal of Low Temperature Physics · doi:10.1023/a:1014808313480 · Cited by 2
Rethinking Renormalization for Quantum Phase TransitionsPreprint
Carteret, H. A. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0405168 · Cited by 4
Power laws in Ising strips: Density-matrix renormalization-group calculations
Drzewiński, A., Szṅajd, J., & Szota, K. (2005) · Physical Review B · doi:10.1103/physrevb.72.014441 · Cited by 2
Wang, Y.-M. (2005) · Applied Mathematics Letters · doi:10.1016/j.aml.2005.04.014 · Cited by 2
Phases and phase transitions in spin-triplet ferromagnetic superconductorsPreprint
Shopova, D. V., & Uzunov, D. I. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0404261 · Cited by 2
Shopova, D. V., & Uzunov, D. I. (2004) · Physics Letters A · doi:10.1016/j.physleta.2004.06.014 · Cited by 2
Direct measurement of relative and collective diffusion in a dilute binary colloidal suspension
Knowles, M. K., Honerkamp‐Smith, A. R., & Marcus, A. H. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1926227 · Cited by 2
Effects of neutral selection on the evolution of molecular speciesPreprint
Newman, M. E. J., & Engelhardt, R. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.adap-org/9712005 · Cited by 2
Self-citationAdiabatic sound velocity in the vicinity of phase transition in magnets
Pawlak, A. (2003) · physica status solidi (b) · doi:10.1002/pssb.200301707 · Cited by 2
Structured psychosocial stress and the US obesity epidemicPreprint
Wallace, R., & Wallace, D. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.q-bio/0312011 · Cited by 2
About the magnetic fluctuation effect on the phase transition to superconducting state in Al
Shopova, D. V., Todorov, T. T., Tsvetkov, T. E., et al. (2002) · Max Planck Institute for Plasma Physics · Cited by 2
Finite-size scaling in systems with long-range interactionPreprint
Chamati, H. (2001) · Cited by 2
Effect of Social Behaviors in the Opinion Dynamics q-Voter ModelPreprint
Muslim, R. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4522251 · Cited by 2
Diffusion spreadability as a probe of the microstructure of complex media across length scales
Torquato, S. (2021) · Physical review. E · doi:10.1103/physreve.104.054102 · Cited by 1
Effective theory building and manifold learning
Freeborn, D. (2025) · Synthese · doi:10.1007/s11229-024-04844-0 · Cited by 2
Dynamical Spreading and Memory Retention of Particle Suspensions under Power Law Potential
Fanto, I., Rosenblum, Y., Harel, O., Zion, M. Y. B., & Oppenheimer, N. (2026) · Physical Review Letters · doi:10.1103/v1nk-pfzj
Dawley, S. J., & Salvatore Torquato, A. (2025) · Physical review. E · doi:10.1103/9wbz-h7t4 · Cited by 1
Higher-order contagion processes in 3.99 dimensions
Meloni, S., Gabrielli, A., & Villegas, P. (2026) · Physical review. E · doi:10.1103/98rn-9x9q · Cited by 1
Critical behavior of a programmable time-crystal lattice gas
Hurtado-Gutiérrez, R., Pérez-Espigares, C., & Hurtado, P. I. (2025) · Physical review. E · doi:10.1103/rx8l-f4ql · Cited by 1
Mazumdar, D., & Das, I. (2025) · Physical review. B./Physical review. B · doi:10.1103/x9wx-vcwv · Cited by 1
Three-dimensional digital core reconstruction from 2D SEM images of heterogeneous shale samples
Feng, Q., Xu, X., Wang, R., et al. (2026) · Computers & Geosciences · doi:10.1016/j.cageo.2026.106119 · Cited by 1
The frequency response of networks as open systems
Nazerian, A., Asllani, M., Tyloo, M., Ku, W. L., & Sorrentino, F. (2026) · Nature Communications · doi:10.1038/s41467-026-68602-1 · Cited by 4
Monte Carlo Simulations of Lipid Bilayers and Liposomes Using Coarse-Grained Models
Wahab, M., Mögel, H. ‐., & Schiller, P. (2011) · Elsevier eBooks · doi:10.1016/b978-0-12-387720-8.00006-6 · Cited by 1
A historical review of optical activity phenomena
Barron, L. D. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511535468.003 · Cited by 3
Field theoretic treatment of an effective action for a model of catalyzed autoamplification
Tchernookov, M., Warmflash, A., & Dinner, A. R. (2010) · Physical Review E · doi:10.1103/physreve.81.011112 · Cited by 1
On the critical specific heat capacity of a classical anharmonic crystal with long-range interaction
Pisanova, E. S., & Ivanov, S. I. (2014) · Journal of Physics Conference Series · doi:10.1088/1742-6596/558/1/012019 · Cited by 1
Emergence of Abstaining in Glauber Opinion Dynamics
Niu, B., & Wei, W. (2013) · Applied Mechanics and Materials · doi:10.4028/www.scientific.net/amm.347-350.3827 · Cited by 1
Specific heat and critical behavior of Tl0.3MoO3 near the Peierls phase transition
Wang, J., Xiong, R., Li, C., et al. (2006) · Solid State Communications · doi:10.1016/j.ssc.2006.06.035 · Cited by 1
Transições de fase sem termodinâmica
Dickman, A. G., Dickman, R., & Barbosa, F. A. (2006) · Revista Brasileira de Ensino de Física · doi:10.1590/s1806-11172006000100004 · Cited by 1
Phase separation of a binary two-dimensional core-softened fluid
Huang, Z., Merlitz, H., & Wu, C. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2202852 · Cited by 1
Phase diagrams and fixed points
Cardy, J. (1996) · Cambridge University Press eBooks · doi:10.1017/cbo9781316036440.005 · Cited by 1
Foundation of SOC in Power Systems
Mei, S., Zhang, X., & Cao, M. (2011) · Springer eBooks · doi:10.1007/978-3-642-16211-4_3 · Cited by 1
Quantum critical behaviour in systems with quenched long-range correlated impurities
Takov, I. P. (2001) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(00)00485-4 · Cited by 1
Gałązka, M., Zieliński, P., Piecha‐Bisiorek, A., et al. (2010) · Phase Transitions · doi:10.1080/01411594.2010.509046 · Cited by 1
Phenomenology of Incompleteness: From Formal Deductions to Mathematics and Physics
Bailly, F., & Longo, G. O. (2008) · Springer eBooks · doi:10.1007/978-88-470-0784-0_13 · Cited by 1
Cardy, J. (1996) · Cambridge University Press eBooks · doi:10.1017/cbo9781316036440.008 · Cited by 1
Formation of Bose-Einstein Condensates
Davis, M. J., Wright, T. M., Gasenzer, T., Gardiner, S. A., & Proukakis, N. P. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316084366.009 · Cited by 8
Is it “natural” to expect economics to become a part of the natural sciences?
Chatterjee, A. (2016) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2016-60157-0 · Cited by 1
Molecules in electric and magnetic fields
Barron, L. D. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511535468.004 · Cited by 1
Kosterlitz-Thouless transition
Nishimori, H., & Ortiz, G. E. (2010) · doi:10.1093/acprof:oso/9780199577224.003.0007 · Cited by 1
Mahakrishnan, S., Chakraborty, S., & Vijay, A. (2016) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.6b06380 · Cited by 1
Wegner, F. (2016) · Journal of Statistical Physics · doi:10.1007/s10955-016-1632-7 · Cited by 1
The Nonlocal Model of Short-Range Wetting
Bernardino, N. R. (2008) · doi:10.25560/1349 · Cited by 1
Classical Monte Carlo Simulation
Santra, S. B., & Ray, P. (2011) · Texts and readings in physical sciences · doi:10.1007/978-93-86279-50-7_4 · Cited by 1
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review