SWhat 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.
Scientific 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
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.
Contributors
- The named authors in the research record · SCIENCE: 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.
- Destruction of long-range order I: Classical systems (1971English translation of1970original)
- Destruction of long-range order II: Quantum systems (1972English translation of1971original)
Provisional WRS assessment, edition 2026-10-23.4. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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