  We revisit the two-dimensional quantum Ising model by computing
renormalization group flows close to its quantum critical point. The low but
finite temperature regime in the vicinity of the quantum critical point is
squashed between two distinct non-Gaussian fixed points: the classical fixed
point dominated by thermal fluctuations and the quantum critical fixed point
dominated by zero-point quantum fluctuations. Truncating an exact flow equation
for the effective action we derive a set of renormalization group equations and
analyze how the interplay of quantum and thermal fluctuations, both
non-Gaussian in nature, influences the shape of the phase boundary and the
region in the phase diagram where critical fluctuations occur. The solution of
the flow equations makes this interplay transparent: we detect finite
temperature crossovers by computing critical exponents and we confirm that the
power law describing the finite temperature phase boundary as a function of
control parameter is given by the correlation length exponent at zero
temperature as predicted in an epsilon-expansion with epsilon=1 by Sachdev,
Phys. Rev. B 55, 142 (1997).
