The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Ferromagnetic Phase Transitions in Random Fields: The Breakdown of Scaling Laws
Abstract
The scaling laws relating the critical exponents characterizing the ferromagnetic phase transition are shown to be modified in the presence of quenched random magnetic fields. The hyperscaling relation $d\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, for example, becomes $(d+{\ensuremath{\lambda}}_{u})\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, where the index ${\ensuremath{\lambda}}_{u}$ is negative and is related to the range of the ferromagnetic exchange interactions. This breakdown of hyperscaling results from a singular dependence of the thermodynamic functions on the scaling field associated with an irrelevant operator.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The renormalization group and the ε expansion
Wilson, K. (1974) · Physics Reports · doi:10.1016/0370-1573(74)90023-4 · Cited by 5,179
Edwards, S. F., & Anderson, P. W. (1975) · Journal of Physics F: Metal Physics · doi:10.1088/0305-4608/5/5/017 · Cited by 3,991
Random-Field Instability of the Ordered State of Continuous Symmetry
Imry, Y., & Ma, S.-K. (1975) · Physical Review Letters · doi:10.1103/physrevlett.35.1399 · Cited by 2,666
Modern Theory of Critical Phenomena
Osborn, H. (1977) · Physics Bulletin · doi:10.1088/0031-9112/28/4/035 · Cited by 1,882
Critical Exponents for Long-Range Interactions
Fisher, M. E., Ma, S.-K., & Nickel, B. G. (1972) · Physical Review Letters · doi:10.1103/physrevlett.29.917 · Cited by 1,236
Wegner, F. J. (1972) · Physical Review B · doi:10.1103/physrevb.5.4529 · Cited by 1,223
Feynman-Graph Expansion for Critical Exponents
Wilson, K. G. (1972) · Physical Review Letters · doi:10.1103/physrevlett.28.548 · Cited by 655
Tricritical Exponents and Scaling Fields
Riedel, E. K., & Wegner, F. (1972) · Physical Review Letters · doi:10.1103/physrevlett.29.349 · Cited by 313
Condensation of the Ideal Bose Gas as a Cooperative Transition
Gunton, J. D., & Buckingham, M. J. (1968) · Physical Review · doi:10.1103/physrev.166.152 · Cited by 138
Ideal Bose Einstein condensation and disorder effects
Lacour-Gayet, P., & Toulouse, G. (1974) · Journal de physique · doi:10.1051/jphys:01974003505042500 · Cited by 94
Cited by
The nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660
Lowering of Dimensionality in Phase Transitions with Random Fields
Aharony, A., Imry, Y., & Ma, S.-K. (1976) · Physical Review Letters · doi:10.1103/physrevlett.37.1364 · Cited by 425
Damgaard, P. H., & Hüffel, H. (1987) · Physics Reports · doi:10.1016/0370-1573(87)90144-x · Cited by 355
Landau theory of quantum spin glasses of rotors and Ising spins
Read, N., Sachdev, S., & Ye, J. (1995) · Physical Review B · doi:10.1103/physrevb.52.384 · Cited by 165
Aharony, O., Komargodski, Z., & Yankielowicz, S. (2016) · Journal of High Energy Physics · doi:10.1007/jhep04(2016)013 · Cited by 23
Metadata
- Authors
- Grinstein, G.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1976-10-04
- Volume
- 37
- Issue
- 14
- Pages
- 944-947
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2012800350
- Cited by
- 276
- References
- 10
- FWCI
- 4.63
- Type
- journal article
- Language
- en
- Open access
- closed
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Ferromagnetic Phase Transitions in Random Fields: The Breakdown of Scaling Laws. https://app.cochat.ai/papers/10.1103/physrevlett.37.944
- The paper
- Grinstein, G. (1976). Ferromagnetic Phase Transitions in Random Fields: The Breakdown of Scaling Laws. Physical Review Letters. https://doi.org/10.1103/physrevlett.37.944
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
