Finite Size Scaling and Long-Range Interactions

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+σ}$ , where $d$ is the spatial dimension and the long-range parameter $σ>0$ . Classical and quantum systems are considered.The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+σ}$, where $d$ is the spatial dimension and the long-range parameter $σ>0$. Classical and quantum systems are considered.

arXiv:cond-mat/0412539Dec 20, 20040 citations

Conformal field theory in the Tomonaga–Luttinger model with the 1/rβlong-range interaction

Hitoshi Inoue, K. Nomura

We attempt to construct U (1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/ r β long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.We attempt to construct U (1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/ r β long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.

arXiv:cond-mat/0310527Journal of Physics A Mathematical and GeneralFeb 15, 200616 citations

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as

1/r^{d+σ}

, where

d

is the spatial dimension and the long-range parameter

σ>0

. Classical and quantum systems are considered.