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Motivated by recent work on local quantum criticality in condensed mattersystems, we study the Lipkin-Meshkov-Glick (LMG) model of nuclear physics as asimple model of a kind of 'quasi-local' quantum criticality. We identify a newcrossover temperature, T*(V,W), between linear and nonlinear dynamics, which isanalogous to the crossover between the renormalized classical and quantumcritical regimes in the condensed-matter case. This temperature T* typicallyvanishes logarithmically as the quantum phase transition is approached, exceptnear the quantum tricritical point where it becomes linear. We also note afurther analogy with condensed-matter quantum criticality: the LMG modelexhibits quantum order-by-disorder phenomena, of the type often associated withphase reconstruction near quantum critical points.

The Lipkin-Meshkov-Glick model: 'quasi-local' quantum criticality in nuclear physics