By solving the Einstein equations of the graviton coupling with a real scalar
dilaton field, we establish a general framework to self-consistently solve the
geometric background with black-hole for any given phenomenological holographic
models. In this framwork, we solve the black-hole background, the corresponding
dilaon field and the dilaton potential for the deformed AdS5 model with a
positive/negative quadratic correction. We systematically investigate the
thermodynamical properties of the deformed AdS5 model with a positive and
negative quadratic correction, respectively, and compare with lattice QCD on
the results of the equation of state, the heavy quark potential, the Polyakov
loop and the spatial Wilson loop. We find that the bulk thermodynamical
properties are not sensitive to the sign of the quadratic correction, and the
results of both deformed holographic QCD models agree well with lattice QCD
result for pure SU(3) gauge theory. However, the results from loop operators
favor a positive quadratic correction, which agree well with lattice QCD
result. Especially, the result from the Polyakov loop excludes the model with a
negative quadratic correction in the warp factor of AdS5.Comment: 26 figures,36 pages,V.3: an appendix,more equations and references
added,figures corrected,published versio