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Two-Dimensional Heisenberg Model with Nonlinear Interactions

Sergio Caracciolo·Andrea Pelissetto
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Abstract

We investigate a two-dimensional classical $N$-vector model with a nonlinear interaction $(1 + \bsigma_i\cdot \bsigma_j)^p$ in the large-N limit. As observed for N=3 by Blöte {\em et al.} [Phys. Rev. Lett. {\bf 88}, 047203 (2002)], we find a first-order transition for $p>p_c$ and no finite-temperature phase transitions for $p < p_c$. For $p>p_c$, both phases have short-range order, the correlation length showing a finite discontinuity at the transition. For $p=p_c$, there is a peculiar transition, where the spin-spin correlation length is finite while the energy-energy correlation length diverges.

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Sergio Caracciolo, Andrea Pelissetto. 2002-03-16. Two-Dimensional Heisenberg Model with Nonlinear Interactions. https://doi.org/10.1103/physreve.66.016120

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