The phase diagram of the O(n) model

Henk W.J. Blöte and Bernard Nienhuis

Physica A: Statistical Mechanics and its Applications, 1989, vol. 160, issue 2, 121-134

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.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:160:y:1989:i:2:p:121-134

DOI: 10.1016/0378-4371(89)90410-X

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