Abstract
We give optimal conditions concerning the range of interactions for the absence of spontaneous breakdown of continuous symmetries for one- and two-dimensional quantum and classical lattice and continuum systems. For a class of models verifying infrared bounds our conditions are necessary and sufficient. Using the same techniques we obtain “a priori” bounds on clustering for systems with continuous symmetry, improving results of Jasnow and Fisher.
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Partially supported by CAPES-PICD.
Partially supported by the CNPq.
Partially supported by N.S.F. under grant MCS 7801433.
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Bonato, C.A., Perez, J.F. & Klein, A. The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems. J Stat Phys 29, 159–175 (1982). https://doi.org/10.1007/BF01020779
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DOI: https://doi.org/10.1007/BF01020779