TY - JOUR
T1 - Plate-Nematic Phase in Three Dimensions
AU - Disertori, Margherita
AU - Giuliani, Alessandro
AU - Jauslin, Ian
N1 - Funding Information:
A.G. and M.D. acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC CoG UniCoSM, grant agreement n.724939). The work of I.J. was supported by The Giorgio and Elena Petronio Fellowship Fund and The Giorgio and Elena Petronio Fellowship Fund II. The work of M.D. was also supported by the German Research Foundation through the Collaborative Research Center 1060 “The Mathematics of Emergent Effects”, project A08. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Funding Information:
A.G. and M.D. acknowledge support from the European Research Council (ERC) under the European Union?s Horizon 2020 research and innovation programme (ERC CoG UniCoSM, grant agreement n.724939). The work of I.J. was supported by The Giorgio and Elena Petronio Fellowship Fund and The Giorgio and Elena Petronio Fellowship Fund II. The work of M.D. was also supported by the German Research Foundation through the Collaborative Research Center 1060 ?The Mathematics of Emergent Effects?, project A08.
Publisher Copyright:
© 2019, The Author(s).
PY - 2020/1/1
Y1 - 2020/1/1
N2 - We consider a system of anisotropic plates in the three-dimensional continuum, interacting via purely hard core interactions. We assume that the particles have a finite number of allowed orientations. In a suitable range of densities, we prove the existence of a uni-axial nematic phase, characterized by long range orientational order (the minor axes are aligned parallel to each other, while the major axes are not) and no translational order. The proof is based on a coarse graining procedure, which allows us to map the plate model into a contour model, and in a rigorous control of the resulting contour theory, via Pirogov-Sinai methods.
AB - We consider a system of anisotropic plates in the three-dimensional continuum, interacting via purely hard core interactions. We assume that the particles have a finite number of allowed orientations. In a suitable range of densities, we prove the existence of a uni-axial nematic phase, characterized by long range orientational order (the minor axes are aligned parallel to each other, while the major axes are not) and no translational order. The proof is based on a coarse graining procedure, which allows us to map the plate model into a contour model, and in a rigorous control of the resulting contour theory, via Pirogov-Sinai methods.
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U2 - 10.1007/s00220-019-03543-z
DO - 10.1007/s00220-019-03543-z
M3 - Article
AN - SCOPUS:85075978482
VL - 373
SP - 327
EP - 356
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -