Long-range order in lattice spin systems

Verbeure, André

doi:10.1088/1751-8113/42/23/232002

Cited by 1 publication

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since then various more precise and more general versions have been considered (see Refs. 300,[306][307][308][309][310][311] ). These considerations of symmetry broken systems are important in order to establish whether or not long-range order is possible in various concrete situation.…”

Section: Bogoliubov's Inequality and The Mermin-wagner Theoremmentioning

confidence: 99%

Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence

Kuzemsky

2010

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

In the present interdisciplinary review we focus on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N. N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in domain of quantum statistical mechanics, quantum field theory and in the quantum physics in general. We discuss the complementary unifying ideas of modern physics, namely: spontaneous symmetry breaking, quantum protectorate and emergence. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical physics. The chief purposes of this paper were to demonstrate the connection and interrelation of these conceptual advances of the many-body physics and to try to show explicitly that those concepts, though different in details, have a certain common features. Several problems in the field of statistical physics of complex materials and systems (e.g. the chirality of molecules) and the foundations of the microscopic theory of magnetism and superconductivity were discussed in relation to these ideas.

show abstract