DOI: https://doi.org/10.30970/jps.11.178
A PHASE TRANSITION IN A QUANTUM ANHARMONIC CRYSTAL
A. Kargol, Y. Kozitsky
Instytut Matematyki UMCS, 20–031 Lublin, Poland
e-mail: akargol@golem.umcs.lublin.pl, jkozi@golem.umcs.lublin.pl
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Journal of Physical Studies 11(2), 178–189 (2007)
DOI: https://doi.org/10.30970/jps.11.178 A PHASE TRANSITION IN A QUANTUM ANHARMONIC CRYSTALA. Kargol, Y. Kozitsky
Instytut Matematyki UMCS, 20–031 Lublin, Poland |
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A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice ${\mathbb Z}^d$ is considered. The anharmonic potential is of a general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\geq 3$, and particle mass as well as interaction intensity are big enough. The proof is based on the representation of local Gibbs states of the model in terms of path measures and thereby on the use of the infrared estimates and the Garsia-Rodemich-Rumsey inequality.
PACS number(s): 63.20.Ry, 64.60.-i