Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Statistical Physics

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

Abel Klein, Lawrence J. Landau, David S. Shucker

Published Nov 1, 1981• 19 citations
Publisher
DOI
10.1007/bf01011431

Related papers

Spontaneous breakdown of symmetry and the generalized coherent states

M. Hongoh, D. Matz

Springer eBooks•Apr 6, 2008•0 citations

Gibbs states and spontaneous symmetry breakdown

Christian Gruber

Springer eBooks•Apr 7, 2008•1 citation

Spontaneous symmetry breakdown and symmetry restoration in the statistical mechanics of a many-boson model

Dalcio Kisling Dacol

Physica A Statistical Mechanics and its Applications•Mar 1, 1980•2 citations

Spontaneous translation symmetry breakdown for quantum lattice systems

Ricardo Lima, Jan Naudts

Journal of Statistical Physics•Apr 1, 1985•0 citations

Absence of continuous symmetry breaking in two-dimensional models of statistical physics

Senya B. Shlosman

Theoretical and Mathematical Physics•Oct 1, 1977•7 citations

Quantum fluctuations in quantum lattice-systems with continuous symmetry 1

Tsutomu Momoi

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems at T = 0. Our analysis is based on Pitaevskii and Stringari’s idea that the uncertainty relation can be employed to show quantum fluctuations. For the one-dimensional systems, it is shown that the ground state is invariant under the continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than |r | −d+1 whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice-systems having not-too-long-range interactions.

•Jan 1, 1996•19 citations
We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems at T = 0. Our analysis is based on Pitaevskii and Stringari’s idea that the uncertainty relation can be employed to show quantum fluctuations. For the one-dimensional systems, it is shown that the ground state is invariant under the continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than |r | −d+1 whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice-systems having not-too-long-range interactions.