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Abstract
Motivated by recent work on local quantum criticality in condensed matter systems,
we study the Lipkin-Meshkov-Glick (LMG) model of nuclear physics as a simple model
of a kind of 'quasi-local' quantum criticality. We identify a new crossover temperature,
T*(V,W), between linear and nonlinear dynamics, which is analogous to the crossover
between the renormalized classical and quantum critical regimes in the condensed-matter
case. This temperature T* typically vanishes logarithmically as the quantum phase
transition is approached, except near the quantum tricritical point where it becomes
linear. We also note a further analogy with condensed-matter quantum criticality:
the LMG model exhibits quantum order-by-disorder phenomena, of the type often associated
with phase reconstruction near quantum critical points.