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The Landau-Ginzburg-Wilson model in 2 and 2+ϵ dimensions at low temperatures

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  • Myerson, Robert J.

Abstract

By introducing a collective variable the two-dimensional Landau-Ginzburg-Wilson model (classical order parameter of non-rigid magnitude) may, if the order parameter dimension exceeds one, be solved at absolute zero. A low temperature expansion about this solution is developed. The low temperature expansion supports the hypothesis that d = 2 systems with a two-component order parameter will have a non-zero critical point, below which the susceptibility diverges, although no symmetry breaking occurs. The leading order temperature dependence of η is determined. In addition an ϵ expansion for systems of spatial dimension 2 + ϵ is developed. The critical exponents, calculated here to lowest order in ϵ, agree with those found for stiff spins.

Suggested Citation

  • Myerson, Robert J., 1978. "The Landau-Ginzburg-Wilson model in 2 and 2+ϵ dimensions at low temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(3), pages 431-449.
    • Handle: RePEc:eee:phsmap:v:90:y:1978:i:3:p:431-449
    DOI: 10.1016/0378-4371(78)90003-1
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    References listed on IDEAS

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    1. Seymour Kaplan, 1966. "Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method," Operations Research, INFORMS, vol. 14(6), pages 1130-1136, December.
    2. Zinn, Karl Georg, 1976. "Hochkonjunktur bei Unterbeschäftigung? Die analytischen Defizite der jüngsten Aufschwungeuphorie," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 56(8), pages 395-403.
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