Quantum spherical description of an Ising spin glass in a transverse field

We study the competition between bond randomness and quantum fluctuation in the infinite-range Ising model in the transverse field Δ relevant for a number of pseudospin and magnetic quantum spin-glass systems. By introducing a mapping of the quantum Hamiltonian of the model onto a soft-spin action we consider it truncated version in a form of the solvable quantized spherical model. The resulting critical phase boundary ${\mathrm{T}}_{\mathrm{crit}}$(Δ) is in considerable agreement with the numerical estimates based on the Trotter-Suzuki and Monte Carlo methods. The equation of state for the system is also given.