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We present exact results for the ground-state and thermodynamic properties ofthe spin-1/2 $XX$ chain with three-site interactions in a random (Lorentzian)transverse field. We discuss the influence of randomness on the quantumcritical behavior known to be present in the nonrandom model. We find that atzero temperature the characteristic features of the quantum phase transition,such as kinks in the magnetization versus field curve, are smeared out byrandomness. However, at low but finite temperatures signatures of the quantumcritical behavior are preserved if the randomness is not too large. Even thequantum critical region may be slightly enlarged for very weak randomness. Inaddition to the exact results for Lorentzian randomness we present a moregeneral discussion of an arbitrarily random transverse magnetic field based onthe inspection of the moments of the density of states.

physical review. b, condensed matter and materials physics

Exact solution of a spin-1/2 $XX$ chain with three-site interactions in  a random transverse field: Influence of randomness on quantum phase  transition