A numerical study of the 3D random interchange and random loop models

Abstract

We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long loops is Poisson-Dirichlet with parameter 1 or 1/2.

11 pages

References in corpus (2)

• Spin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study
• Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems

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