Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

Details Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

2004-09-21

arxiv.org/abs/cond-mat/0409536v1

Nucl.Phys.B707:458-492,2005

Physics

Condensed Matter

Statistical Mechanics

34 pages, 1 figure

Scientific paper

10.1016/j.nuclphysb.2004.11.027

We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction $W(\bsigma_i\cdot \bsigma_j)$ in the large-N limit, focusing on the finite-temperature transition point at which energy-energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as $1/N^{3/2}$ along the magnetic direction and as 1/N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for $N=\infty$

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