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Susceptibility of the transverse field Ising model on the square lattice iscalculated numerically in the paramagnetic phase in a wide range oftemperatures and transverse fields. An expression with one constant $\pi$, thatdetermines both the critical exponent $\gamma$ and the critical transversefield, compellingly represents the data asymptotically near the quantumcritical point, except for a narrow classical region close to the phasetransition line, and shows two crossovers as temperature varies.