Journal ArticleDOI
The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
Jürg Fröhlich,Thomas Spencer +1 more
TLDR
In this paper, the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤ n −1 model in two dimensions was proved.Abstract:
We rigorously establish the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤ
n
models, forn large enough, and in the Coulomb lattice gas, in two dimensions. Our proof is based on an inductive expansion of the Coulomb gas in the sine-Gordon representation, extending over all possible distance scales, which expresses that gas as a convex superposition of dilute gases of neutral molecules whose activities are small if β is sufficiently large. Such gases are known not to exhibit screening. Abelian spin systems are related to a Coulomb gas by means of a duality transformation.read more
Citations
More filters
Journal ArticleDOI
The Potts model
TL;DR: In this paper, a tutorial review on the Potts model is presented aimed at bringing out the essential and important properties of the standard Potts models, focusing on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective.
Journal ArticleDOI
The renormalization group and critical phenomena
TL;DR: In this article, a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena is given, following roughly a summary exposition given in 1972.
Journal ArticleDOI
Absence of diffusion in the Anderson tight binding model for large disorder or low energy
Jürg Fröhlich,Thomas Spencer +1 more
TL;DR: In this article, it was shown that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on Ω v ≥ 0, with probability 1.
Journal ArticleDOI
Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
TL;DR: In this article, the conceptual foundations of the renormalization-group (RG) formalism are considered and rigorous theorems on the regularity properties and possible pathologies of the RG map are presented.
Journal ArticleDOI
Constructive proof of localization in the Anderson tight binding model
TL;DR: In this paper, it was shown that for large disorder or near the band tails, the spectrum of the Anderson tight binding Hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues.
References
More filters
Journal ArticleDOI
Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model
TL;DR: In this paper, the authors studied the effect of symmetry-breaking crystalline fields on the isotropic planar model at low temperatures by means of renormalization theory and a series of exact transformations.
Journal ArticleDOI
Observables at infinity and states with short range correlations in statistical mechanics
Oscar E. Lanford,David Ruelle +1 more
TL;DR: In this paper, the authors show that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a state has finite range correlations if the corresponding cyclic representation does.
Journal ArticleDOI
Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
Journal ArticleDOI
Symmetry-breaking aspects of the roughening transition in gauge theories
TL;DR: In this article, it was shown that the associated Goldstone bosons live effectively in 1 + 1 dimensions and therefore, by the Mermin-Wagner-Coleman theorem, destabilize the flux tube.
Journal ArticleDOI
Exactly solvable model for the roughening transition of a crystal surface
TL;DR: In this paper, an exact solvable model of the crystal-vacuum interface is constructed which exhibits a roughening transition and is isomorphic to the symmetric six-vertex model.
Related Papers (5)
Ordering, metastability and phase transitions in two-dimensional systems
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
N. D. Mermin,Herbert Wagner +1 more