The two-dimensional interacting electron gas at Landau level filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and temperature $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on its thermodynamic properties using a many-body perturbation theory approach and concentrating on the recently measured temperature dependence of the spin magnetization. We discuss the interplay of collective and single-particle aspects of the physics and the opportunities for progress in our understanding of itinerant electron ferromagnetism presented by quantum Hall ferromagnets.The two-dimensional interacting electron gas at Landau level filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and temperature $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on its thermodynamic properties using a many-body perturbation theory approach and concentrating on the recently measured temperature dependence of the spin magnetization. We discuss the interplay of collective and single-particle aspects of the physics and the opportunities for progress in our understanding of itinerant electron ferromagnetism presented by quantum Hall ferromagnets.

arXiv:cond-mat/9510021Physical Review LettersApr 22, 199631 citations

Criticality in the two-dimensional random-bond Ising model

Sora Cho, Matthew P. A. Fisher

The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the random Ising phase transition. The values are consistent with recent estimates obtained from high-temperature series.The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the random Ising phase transition. The values are consistent with recent estimates obtained from high-temperature series.

arXiv:cond-mat/9607175Physical review. B, Condensed matterJan 1, 1997101 citations

First-order phase transitions in a quantum Hall ferromagnet

Vincenzo Piazza, Vittorio Pellegrini, Fabio Beltram +3 more

arXiv:cond-mat/9906294NatureDec 1, 1999136 citations

Interaction and dimensionality in the quantum Hall physics

Hideo Aoki

arXiv:cond-mat/0310057Physica E Low-dimensional Systems and NanostructuresDec 1, 20033 citations

Two-dimensional random-bond Ising model, free fermions, and the network model

Florian Merz, J. T. Chalker

We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions. The RBIM transforms in this way to a localization problem belonging to one of a set of nonstandard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalization transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width M is proportional to ${M}^{3},$ and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM the free energy, typical correlation lengths in quasi-one dimension for both the spin and the disorder operators, and the even powers of spin-spin correlation functions and their disorder averages. We examine in detail the square-lattice, nearest-neighbor $\ifmmode\pm\else\textpm\fi{}J$ RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability $1\ensuremath{-}p.$ Studying temperatures $T>~0.4J,$ we obtain precise coordinates in the $p\ensuremath{-}T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point.We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions. The RBIM transforms in this way to a localization problem belonging to one of a set of nonstandard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalization transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width M is proportional to ${M}^{3},$ and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM the free energy, typical correlation lengths in quasi-one dimension for both the spin and the disorder operators, and the even powers of spin-spin correlation functions and their disorder averages. We examine in detail the square-lattice, nearest-neighbor $\ifmmode\pm\else\textpm\fi{}J$ RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability $1\ensuremath{-}p.$ Studying temperatures $T>~0.4J,$ we obtain precise coordinates in the $p\ensuremath{-}T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point.

arXiv:cond-mat/0106023Physical review. B, Condensed matterJan 15, 2002143 citations

The two-dimensional interacting electron gas at Landau level filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and temperature

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on its thermodynamic properties using a many-body perturbation theory approach and concentrating on the recently measured temperature dependence of the spin magnetization. We discuss the interplay of collective and single-particle aspects of the physics and the opportunities for progress in our understanding of itinerant electron ferromagnetism presented by quantum Hall ferromagnets.

{M}^{3},

and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM the free energy, typical correlation lengths in quasi-one dimension for both the spin and the disorder operators, and the even powers of spin-spin correlation functions and their disorder averages. We examine in detail the square-lattice, nearest-neighbor $\ifmmode\pm\else\textpm\fi{}J$ RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability $1\ensuremath{-}p.$ Studying temperatures

T>~0.4J,

we obtain precise coordinates in the $p\ensuremath{-}T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point.