  The recently developed tensor renormalization-group (TRG) method provides a
highly precise technique for deriving thermodynamic and critical properties of
lattice Hamiltonians. The TRG is a local coarse-graining transformation, with
the elements of the tensor at each lattice site playing the part of the
interactions that undergo the renormalization-group flows. These tensor flows
are directly related to the phase diagram structure of the infinite system,
with each phase flowing to a distinct surface of fixed points. Fixed-point
analysis and summation along the flows give the critical exponents, as well as
thermodynamic functions along the entire temperature range. Thus, for the
ferromagnetic triangular lattice Ising model, the free energy is calculated to
better than 10^-5 along the entire temperature range. Unlike previous
position-space renormalization-group methods, the truncation (of the tensor
index range D) in this general method converges under straightforward and
systematic improvements. Our best results are easily obtained with D = 24,
corresponding to 4624-dimensional renormalization-group flows.
