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The phase diagram of the O(n) model

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  • Blöte, Henk W.J.
  • Nienhuis, Bernard

Abstract

We investigate the properties of the zero-field O(n) model on the honeycomb lattice outside the range of presently available exact solutions. To this purpose, we make use of finite-size scaling and transfer-matrix techniques. Our results confirm the expected phase diagram of the O(n) model in the range 0⩽n<2. It consists of a disordered phase, separated by a second order transition from a low-temperature phase with algebraically decaying correlations. We confirm that in this low-temperature phase the exponents are independent of the temperature. More significantly we find evidence for this same universal behaviour even in the case n=2. This contrasts with the temperature dependent exponents of the generic XY model. Our numerical evidence in this case is supported by arguments based on a mapping from the O(n=2) model to the Ashkin-Teller model on the triangular lattice.

Suggested Citation

  • Blöte, Henk W.J. & Nienhuis, Bernard, 1989. "The phase diagram of the O(n) model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(2), pages 121-134.
    • Handle: RePEc:eee:phsmap:v:160:y:1989:i:2:p:121-134
    DOI: 10.1016/0378-4371(89)90410-X
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    1. repec:cai:popine:popu_p1987_42n4-5_0746 is not listed on IDEAS
    2. Blöte, H.W.J & Nightingale, M.P, 1982. "Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 405-465.
    3. 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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