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We study an infinite range ferromagnetic Ising model in the presence of atransverse magnetic field which exhibits a quantum paramagnetic-ferromagneticphase transition at a critical value of the transverse field. In thethermodynamic limit, the low-temperature properties of this model are dominatedby the behavior of a single large classical spin governed by an anisotropicHamiltonian. Using this property, we study the quench and AC dynamics of themodel both numerically and analytically, and develop a correspondence betweenthe classical phase space dynamics of a single spin and the quantum dynamics ofthe infinite-range ferromagnetic Ising model. In particular, we compare thebehavior of the equal-time order parameter correlation function both near toand away from the quantum critical point in the presence of a quench or ACtransverse field. We explicitly demonstrate that a clear signature of thequantum critical point can be obtained by studying the AC dynamics of thesystem even in the classical limit. We discuss possible realizations of ourmodel in experimental systems.Comment: Revtex4, 10 pages including 10 figures; corrected a sign error in Eq.  32; this is the final published versio

Infinite-range Ising ferromagnet in a time-dependent transverse magnetic field: Quench and ac dynamics near the quantum critical point