Showing papers by "Jürg Fröhlich published in 1977"
Journal Article•
TL;DR: In this article, a general theorem is presented which says that from a sequence of Euclidean Green's functions satisfying a special form of the Osterwalder-Schrader axioms a local net of observable algebras satisfying all the Haag-Kastler axiomas can be reconstructed.
Abstract: A general theorem is presented which says that from a sequence of Euclidean Green’s functions satisfying a special form of the Osterwalder-Schrader axioms a local net of observable algebras satisfying all the Haag-Kastler axioms can be reconstructed. In the course of the proof a new sufficient condition for the bounded functions of two commuting, unbounded selfadjoint operators to commute is derived.
47 citations
TL;DR: The two-dimensional anisotropie, the nearest neighbor Heisenberg model on a square lattice, both quantum and classical, has been shown rigorously to have a phase transition in the sense that the spontaneous magnetization is positive at low temperatures as discussed by the authors.
Abstract: The two-dimensional anisotropie, nearest-neighbor Heisenberg model on a square lattice, both quantum and classical, has been shown rigorously to have a phase transition in the sense that the spontaneous magnetization is positive at low temperatures. This is so for all anisotropies. An analogous result (staggered polarization) holds for the antiferromagnet in the classical case; in the quantum case it holds if the anisotropy is large enough (depending on the single-site spin).
37 citations
01 Jan 1977
TL;DR: A survey of some mathematically rigorous results concerning phase transitions and symmetry breaking in statistical mechanics and quantum field theory can be found in this paper, where the authors apply a variant of the Peierls argument [GJS3] to prove that there is a phase transition in the two-dimensional, anisotropic (φ·→φ)2 quantum field model in two dimensions.
Abstract: These lectures are a survey of some mathematically rigorous results concerning phase transitions and symmetry breaking in statistical mechanics and quantum field theory. This subject has a rather long history: The first results on phase transitions were obtained by R. Peierls in 1936, [Pe]. He showed that the Ising model in two or more dimensions has spontaneous magnetization at low temperatures. His argument was later reformulated in various ways and applied to many model systems. See the references in [Gr]. We shall apply a variant of the Peierls argument [GJS3] to prove that there is a phase transition in the two dimensional, anisotropic (→φ·→φ)2 quantum field model in two dimensions and we explain how, in this model, a phase transition gives rise to soliton sectors. We show that the mass gap on the soliton sector is bounded below by the “surface tension” of this model.
14 citations