  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.
