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Fractal Structure of High-Temperature Graphs of O($N$) Models in Two Dimensions

Wolfhard Janke·Adriaan M. J. Schakel
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Abstract

The fractal structure and critical properties of the high-temperature graphs of the two-dimensional O($N)$ model close to criticality are investigated. Based on Monte Carlo simulations, De Gennes' results for polymer chains, corresponding to the limit $N \to 0$, are generalized to random loops for arbitrary $-2 \leq N \leq 2$. The loops are also studied close to their tricritical point, known as the $Θ$ point in the context of polymers, where they collapse. The corresponding fractal dimensions are argued to be in one-to-one correspondence with those at the critical point, leading to an analytic prediction for the magnetic scaling dimension at the O($N)$ tricritical point.

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Wolfhard Janke, Adriaan M. J. Schakel. 2005-09-26. Fractal Structure of High-Temperature Graphs of O($N$) Models in Two Dimensions. https://doi.org/10.1103/physrevlett.95.135702

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