{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "berezinskii-planar-algebraic-order-vortex-superfluidity-1970", "title": "Berezinskii: algebraic order and vortex physics in two-dimensional planar systems", "summary": "A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions.", "boundary": "These are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. This record does not absorb the separate Kosterlitz–Thouless 1973 work, later RG theory, rigorous proofs or measurements.", "area": "Low-dimensional statistical physics", "topic": "Physics", "year": 1970, "lane": "HUMAN", "result": "THEORY", "package_id": "berezinskii-planar-algebraic-order-vortex-superfluidity-1970", "target": { "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "content_hash": "sha256:94785f22d69fb94882a0700ca5c9270341e60c6530bcaeb9302f47a27302c2f1" }, "humans": [ "V. L. Berezinskii" ], "authors_complete": true, "human_role_note": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. 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Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions.", "scope": "A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions. These are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. 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Berezinskii", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "Destruction of long-range order I: Classical systems (1971English translation of1970original)", "url": "https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Destruction of long-range order I: Classical systems (1971English translation of1970original)", "url": "https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9" } }, { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-1", "kind": "source_reference", "source": { "citation": "Destruction of long-range order II: Quantum systems (1972English translation of1971original)", "url": "https://inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "These are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. This record does not absorb the separate Kosterlitz–Thouless 1973 work, later RG theory, rigorous proofs or measurements.", "domain": "Low-dimensional statistical physics" }, "sources": [ { "citation": "Destruction of long-range order I: Classical systems (1971English translation of1970original)", "url": "https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9" }, { "citation": "Destruction of long-range order II: Quantum systems (1972English translation of1971original)", "url": "https://inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259" } ], "statement": "# Berezinskii: algebraic order and vortex physics in two-dimensional planar systems\n\n## Order can fade slowly rather than vanish at once\n\nImagine arrows placed on a large flat grid. Nearby arrows can strongly prefer similar directions even when the entire grid has no permanent common direction. The distinction is between local agreement, correlations over a distance and true long-range order. Berezinskii’s work explores how two-dimensional planar systems can keep a slowly fading pattern without conventional spontaneous phase-symmetry breaking.\n\n## A power law keeps a long tail\n\nA correlation function measures how strongly separated locations remain related. In the low-temperature planar description, it can decay as a power of distance rather than exponentially. For a classroom illustration, choose the function C(r) equal to one over the cube root of r, for r at least one in chosen units. At r equal to one it is one; at eight it is one half; at sixty-four it is one quarter. The function tends to zero, so this example has no nonzero limiting correlation, yet its tail is long.\n\n## Why vortices matter\n\nA planar angle can wind through a full turn around a loop. Such winding configurations are vortices, and cannot always be captured by treating every angle difference as an arbitrarily small fluctuation. The follow-up relates vortices to a logarithmically interacting gas and connects the low-temperature phase with stiffness and superfluid response. Stiffness describes the energy cost of a gentle twist. These ideas do not require assuming a conventional condensate order parameter remains nonzero at infinite separation.\n\n## Read a historical theory with its corrections\n\nThe source family begins with Russian work in 1970 and continues in 1971; the inspected primary English translations appeared in 1971 and 1972. The follow-up explicitly revises an earlier susceptibility-based phase criterion. Other original assertions must not be substituted for later universal-jump theory or modern rigorous results. The assessment here concerns planar algebraic-order and vortex/stiffness ideas, rather than accepting every isotropic or arbitrary-group extension in the papers.\n\n## A small and honest continuation\n\nAsk your agent to compare three defined curves: a nonzero constant, an exponential decay and a power-law decay. State which can represent nonzero long-range order under that definition, and which merely decays slowly. Label every curve as a teaching choice. A useful source task could trace one historical correction across the two papers and explain its meaning without converting a finite plot into evidence for a thermodynamic phase transition.\n\n## Scientific scope\n\nThese are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. This record does not absorb the separate Kosterlitz–Thouless 1973 work, later RG theory, rigorous proofs or measurements.\n\n## Sources for this explanation\n\n- [Destruction of long-range order I: Classical systems (1971English translation of1970original)](https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9): Pinned original contribution and stated hypotheses or experimental limits.\n- [Destruction of long-range order II: Quantum systems (1972English translation of1971original)](https://inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259): Pinned original contribution and stated hypotheses or experimental limits.\n", "summary": "A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions.", "title": "Berezinskii: algebraic order and vortex physics in two-dimensional planar systems" }, "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "source_ref": { "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "content_hash": "sha256:94785f22d69fb94882a0700ca5c9270341e60c6530bcaeb9302f47a27302c2f1" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:a48082b572e9eb636ecffe6e0cd4579ee7b584f65b13f0ed5ba0ac3c6cfe7569" }, "target": { "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "content_hash": "sha256:94785f22d69fb94882a0700ca5c9270341e60c6530bcaeb9302f47a27302c2f1" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "berezinskii-planar-algebraic-order-vortex-superfluidity-1970", "entry_id": "berezinskii-planar-algebraic-order-vortex-superfluidity-1970", "revision": 1, "title": "Berezinskii: algebraic order and vortex physics in two-dimensional planar systems", "context": "Low-dimensional statistical physics", "track": "Reusable scientific method, experimental result or historical framework", "band": "S", "modifier": "-", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-23", "evidence_cutoff": "2026-10-23", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions.", "scope": "A two-dimensional system can have slowly decaying correlations without settling into conventional long-range order. Berezinskii’s 1970 and 1971 theoretical work, published in English translation in 1971 and 1972, develops this low-temperature picture for planar systems. The follow-up connects vortices to a logarithmically interacting gas and describes stiffness and superfluid response. It also corrects an earlier phase criterion. Later Kosterlitz–Thouless theory, universal-jump results and experiments remain separate contributions. These are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. This record does not absorb the separate Kosterlitz–Thouless 1973 work, later RG theory, rigorous proofs or measurements.", "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. These are historical theoretical calculations and physical arguments under the stated low-temperature, long-wavelength, interaction-range and model assumptions, not experimental observations or an exact solution of every continuous-symmetry system. PartII explicitly corrects PartI's use of infinite susceptibility as a phase criterion. Its formula rho_s(Tc)=0 is preserved as an original historical assertion, not assigned the later universal-jump result. The isotropic Heisenberg extension and arbitrary-group assertions are not promoted here into a rigorous general finite-temperature algebraic-order theorem. This record does not absorb the separate Kosterlitz–Thouless 1973 work, later RG theory, rigorous proofs or measurements.", "references": [ { "title": "Destruction of long-range order I: Classical systems (1971English translation of1970original)", "url": "https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." }, { "title": "Destruction of long-range order II: Quantum systems (1972English translation of1971original)", "url": "https://inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." } ], "roles": [ { "who": "The named authors in the research record", "credit": "SCIENCE", "did": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred." } ], "target": { "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "content_hash": "sha256:94785f22d69fb94882a0700ca5c9270341e60c6530bcaeb9302f47a27302c2f1" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "260000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "berezinskii-planar-algebraic-order-vortex-superfluidity-1970", "target": { "record_id": "urn:uuid:c6a496ac-c3c7-4c19-af0b-5cbbcc07ad40", "version": 1, "content_hash": "sha256:94785f22d69fb94882a0700ca5c9270341e60c6530bcaeb9302f47a27302c2f1" }, "sections": [ { "title": "Order can fade slowly rather than vanish at once", "text": "Imagine arrows placed on a large flat grid. Nearby arrows can strongly prefer similar directions even when the entire grid has no permanent common direction. The distinction is between local agreement, correlations over a distance and true long-range order. Berezinskii’s work explores how two-dimensional planar systems can keep a slowly fading pattern without conventional spontaneous phase-symmetry breaking." }, { "title": "A power law keeps a long tail", "text": "A correlation function measures how strongly separated locations remain related. In the low-temperature planar description, it can decay as a power of distance rather than exponentially. For a classroom illustration, choose the function C(r) equal to one over the cube root of r, for r at least one in chosen units. At r equal to one it is one; at eight it is one half; at sixty-four it is one quarter. The function tends to zero, so this example has no nonzero limiting correlation, yet its tail is long." }, { "title": "Why vortices matter", "text": "A planar angle can wind through a full turn around a loop. Such winding configurations are vortices, and cannot always be captured by treating every angle difference as an arbitrarily small fluctuation. The follow-up relates vortices to a logarithmically interacting gas and connects the low-temperature phase with stiffness and superfluid response. Stiffness describes the energy cost of a gentle twist. These ideas do not require assuming a conventional condensate order parameter remains nonzero at infinite separation." }, { "title": "Read a historical theory with its corrections", "text": "The source family begins with Russian work in 1970 and continues in 1971; the inspected primary English translations appeared in 1971 and 1972. The follow-up explicitly revises an earlier susceptibility-based phase criterion. Other original assertions must not be substituted for later universal-jump theory or modern rigorous results. The assessment here concerns planar algebraic-order and vortex/stiffness ideas, rather than accepting every isotropic or arbitrary-group extension in the papers." }, { "title": "A small and honest continuation", "text": "Ask your agent to compare three defined curves: a nonzero constant, an exponential decay and a power-law decay. State which can represent nonzero long-range order under that definition, and which merely decays slowly. Label every curve as a teaching choice. A useful source task could trace one historical correction across the two papers and explain its meaning without converting a finite plot into evidence for a thermodynamic phase transition." } ], "references": [ { "title": "Destruction of long-range order I: Classical systems (1971English translation of1970original)", "url": "https://inspirehep.net/files/f55503250f690969aedfda4ceaf9b4f9", "locator": "Pinned original contribution and stated hypotheses or experimental limits." }, { "title": "Destruction of long-range order II: Quantum systems (1972English translation of1971original)", "url": "https://inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259", "locator": "Pinned original contribution and stated hypotheses or experimental limits." } ] }, "reading_status": "EXPLANATORY_GUIDE" }