We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction $V(\stackrel{\ensuremath{\rightarrow}}{s},{\stackrel{\ensuremath{\rightarrow}}{s}}^{\ensuremath{'}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2K[(1+\stackrel{\ensuremath{\rightarrow}}{s}\ifmmode \dot{}\else \.{}\fi{}{\stackrel{\ensuremath{\rightarrow}}{s}}^{\ensuremath{'}})/2{]}^{p}$. The analogous nonlinear interaction for the $\mathrm{XY}$ model was introduced by Domany, Schick, and Swendsen, who find that for large $p$ the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard $(p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1)$ Heisenberg model has no phase transition, for large enough $p$ a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction $V(\stackrel{\ensuremath{\rightarrow}}{s},{\stackrel{\ensuremath{\rightarrow}}{s}}^{\ensuremath{'}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2K[(1+\stackrel{\ensuremath{\rightarrow}}{s}\ifmmode \dot{}\else \.{}\fi{}{\stackrel{\ensuremath{\rightarrow}}{s}}^{\ensuremath{'}})/2{]}^{p}$. The analogous nonlinear interaction for the $\mathrm{XY}$ model was introduced by Domany, Schick, and Swendsen, who find that for large $p$ the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard $(p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1)$ Heisenberg model has no phase transition, for large enough $p$ a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.

arXiv:cond-mat/0201174Physical Review LettersJan 14, 200245 citations

Analytical study of the one-dimensional Heisenberg model

豪加藤

Jan 1, 20040 citations

Classical one-dimensional Heisenberg model with an interaction of finite range

T. Morita, T. Horiguchi

Physica A Statistical Mechanics and its ApplicationsJan 1, 19767 citations

Anomalous Finite Size Spectrum in the S=1/2 Two Dimensional Heisenberg Model

C. Lavalle, Sandro Sorella, Alberto Parola

We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin $S$ . By quantum Monte Carlo simulation we compute this spectrum for Heisenberg models with local moments $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ , $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ , and $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$ . We conclude that the nonlinear $\ensuremath{\sigma}$ model prediction for the low energy spectrum is always verified for a large enough system size. However, the crossover to the correct scaling regime is particularly slow just for the $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ Heisenberg model. The possible detection of this unexpected anomaly with finite temperature experiments on $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ isotropic quantum antiferromagnets is also discussed.We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin $S$. By quantum Monte Carlo simulation we compute this spectrum for Heisenberg models with local moments $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$, $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, and $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$. We conclude that the nonlinear $\ensuremath{\sigma}$ model prediction for the low energy spectrum is always verified for a large enough system size. However, the crossover to the correct scaling regime is particularly slow just for the $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ Heisenberg model. The possible detection of this unexpected anomaly with finite temperature experiments on $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ isotropic quantum antiferromagnets is also discussed.

arXiv:cond-mat/9709174Physical Review LettersFeb 23, 199816 citations

Two-dimensional Heisenberg model with nonlinear interactions

Sergio Caracciolo A, Andrea Pelissetto C

We investigate a two-dimensional classical N-vector model with a nonlinear interaction (1+sigma(i) x sigma(j))(p) in the large-N limit. As observed for N=3 by Blöte et al. [Phys. Rev. Lett. 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.We investigate a two-dimensional classical N-vector model with a nonlinear interaction (1+sigma(i) x sigma(j))(p) in the large-N limit. As observed for N=3 by Blöte et al. [Phys. Rev. Lett. 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.

arXiv:cond-mat/0202506Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 24, 200217 citations

\mathrm{XY}

model was introduced by Domany, Schick, and Swendsen, who find that for large

p

the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard

(p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1)

Heisenberg model has no phase transition, for large enough

p

a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.

We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin

S

. By quantum Monte Carlo simulation we compute this spectrum for Heisenberg models with local moments

s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

, and

s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2

. We conclude that the nonlinear $\ensuremath{\sigma}$ model prediction for the low energy spectrum is always verified for a large enough system size. However, the crossover to the correct scaling regime is particularly slow just for the

s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

Heisenberg model. The possible detection of this unexpected anomaly with finite temperature experiments on

s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

isotropic quantum antiferromagnets is also discussed.