{"doi":"10.1038/srep45004","title":"Continuously Varying Critical Exponents Beyond Weak Universality","abstract":"<jats:title>Abstract</jats:title><jats:p>Renormalization group theory does not restrict the form of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., <jats:italic>β, γ, ν</jats:italic>) vary keeping others (e.g., <jats:italic>δ, η</jats:italic>) fixed. Here we report ferromagnetic phase transition in (Sm<jats:sub>1−y</jats:sub>Nd<jats:sub>y</jats:sub>)<jats:sub>0.52</jats:sub>Sr<jats:sub>0.48</jats:sub>MnO<jats:sub>3</jats:sub> (0.5 ≤ <jats:italic>y</jats:italic> ≤ 1) single crystals where all three exponents <jats:italic>β, γ, δ</jats:italic> vary with Nd concentration <jats:italic>y.</jats:italic> Such a variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multi-criticality.</jats:p>","journal":"Scientific Reports","year":2017,"id":673268,"datarank":0.47032413238937254,"base_score":3.1354942159291497,"endowment":3.1354942159291497,"self_citation_contribution":0.47032413238937254,"citation_network_contribution":0.0,"self_endowment_contribution":0.47032413238937254,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":22,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1387365,"name":"P. Sarkar","orcid":null,"position":1,"is_corresponding":false},{"id":1759071,"name":"A. Midya","orcid":null,"position":2,"is_corresponding":false},{"id":1476650,"name":"P. Mandal","orcid":null,"position":3,"is_corresponding":false},{"id":1759072,"name":"P. K. Mohanty","orcid":null,"position":4,"is_corresponding":false},{"id":1570728,"name":"N. Khan","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Continuously Varying Critical Exponents Beyond Weak Universality","abstract":"<jats:title>Abstract</jats:title><jats:p>Renormalization group theory does not restrict the form of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., <jats:italic>β, γ, ν</jats:italic>) vary keeping others (e.g., <jats:italic>δ, η</jats:italic>) fixed. Here we report ferromagnetic phase transition in (Sm<jats:sub>1−y</jats:sub>Nd<jats:sub>y</jats:sub>)<jats:sub>0.52</jats:sub>Sr<jats:sub>0.48</jats:sub>MnO<jats:sub>3</jats:sub> (0.5 ≤ <jats:italic>y</jats:italic> ≤ 1) single crystals where all three exponents <jats:italic>β, γ, δ</jats:italic> vary with Nd concentration <jats:italic>y.</jats:italic> Such a variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multi-criticality.</jats:p>","is_dataset_classified":null,"base_score":3.1354942159291497,"endowment":3.1354942159291497,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"28327622","pmcid":"PMC5361157","openalex_id":"https://openalex.org/W2962977475","authors":[],"funders":[],"total_grants":0,"fwci":0.7215,"citation_percentile":0.66832198,"influential_citations":0,"citation_trend":[{"year":2017,"count":2},{"year":2018,"count":4},{"year":2019,"count":2},{"year":2020,"count":1},{"year":2022,"count":2},{"year":2023,"count":4},{"year":2024,"count":3},{"year":2025,"count":1},{"year":2026,"count":3}],"oa_status":"gold","license":"cc-by","oa_locations":[{"url":"https://www.nature.com/articles/srep45004.pdf","host_type":"journal"},{"url":"https://www.nature.com/articles/srep45004.pdf","host_type":"publisher"},{"url":"https://www.nature.com/articles/srep45004","host_type":"publisher"},{"url":"https://doi.org/10.1038/srep45004","host_type":"journal"},{"url":"https://pubmed.ncbi.nlm.nih.gov/28327622","host_type":"repository"},{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5361157","host_type":"repository"},{"url":"https://europepmc.org/articles/PMC5361157","host_type":"Europe_PMC"},{"url":"https://europepmc.org/articles/PMC5361157?pdf=render","host_type":"Europe_PMC"}],"fields_of_study":["Magnetic and transport properties of perovskites and related materials","Theoretical and Computational Physics","High-pressure geophysics and materials"],"mesh_terms":[],"keywords":["Universality (dynamical systems)","Renormalization group","Critical exponent","Critical phenomena","Statistical physics","Scaling","Phase transition","Mathematics","Percolation critical exponents","Criticality","Self-organized criticality","Physics","Mathematical physics","Condensed matter physics","Geometry"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-16T12:53:24.497669Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}