We present a physical interpretation of a number of exotic exponents of the two-dimensional Ising model, i.e., exponents that do have a conformal classification, but outside the unitary grid. They describe the scaling behavior of geometric properties of Ising and random clusters. For instance, the probability that two spins at a distance r lie on the perimeter of the same Ising cluster decays as ${\mathit{r}}^{\mathrm{\ensuremath{-}}5/4}$ at criticality. These results are obtained via mappings on the Coulomb gas. A part of the Coulomb gas scenario is verified by means of finite-size scaling of transfer-matrix results.We present a physical interpretation of a number of exotic exponents of the two-dimensional Ising model, i.e., exponents that do have a conformal classification, but outside the unitary grid. They describe the scaling behavior of geometric properties of Ising and random clusters. For instance, the probability that two spins at a distance r lie on the perimeter of the same Ising cluster decays as ${\mathit{r}}^{\mathrm{\ensuremath{-}}5/4}$ at criticality. These results are obtained via mappings on the Coulomb gas. A part of the Coulomb gas scenario is verified by means of finite-size scaling of transfer-matrix results.

Physical Review LettersJun 8, 199225 citations

Spin and charge fluctuations of the two-dimensional Hubbard model

Yasushi Shiina

Abstracts of the meeting of the Physical Society of Japan. Sectional meetingSep 12, 19950 citations

Charge and spin order in one dimensional systems with long range Coulomb interaction

M. Belen Valenzuela, S. Fratini, D. Baeriswyl

APSMar 1, 20040 citations

Analytic approach to the ground-state energy of charged anyon gases

B. Abdullaev, U. Rößler, M.M. Musakhanov

We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters ($\ensuremath{\nu}$ and ${r}_{s}$ , respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large ${r}_{s}$ (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small ${r}_{s}$ . The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if ${r}_{s}>1$ . For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters ($\ensuremath{\nu}$ and ${r}_{s}$, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large ${r}_{s}$ (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small ${r}_{s}$. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if ${r}_{s}>1$. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.

arXiv:cond-mat/0701219Physical Review BAug 3, 20077 citations

Some critical properties of a planar model via the eigenstates of a fermion system

Trong Tuong Truong, K. D. Schotte

We show that a soluble Hamiltonian for interacting fermions in one-dimensional conductors generates a classical double Coulomb gas of "electric" and "magnetic" charges and thereby establishes its equivalence with the generalized Villain model in the presence of a fourfold symmetry-breaking term recently studied by L. P. Kadanoff. We use the exact solution of the fermion model to demonstrate how the eight-vertex structure of the mutual fermion scatterings controls its critical behavior.We show that a soluble Hamiltonian for interacting fermions in one-dimensional conductors generates a classical double Coulomb gas of "electric" and "magnetic" charges and thereby establishes its equivalence with the generalized Villain model in the presence of a fourfold symmetry-breaking term recently studied by L. P. Kadanoff. We use the exact solution of the fermion model to demonstrate how the eight-vertex structure of the mutual fermion scatterings controls its critical behavior.

Physical review. B, Condensed matterNov 1, 19814 citations

Critical behavior of 3d Ising and 2d XY spin models

CLIVE F. BAILLIE, Rajan Gupta

Nuclear Physics B - Proceedings SupplementsMay 1, 19914 citations

{r}_{s}

, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large

{r}_{s}

(the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small

{r}_{s}

. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if

{r}_{s}>1

. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.