  We report measurements of the low temperature magnetization $M$ and specific
heat $C$ as a function of temperature and magnetic field of the
quasi-one-dimensional spin chain, heavy fermion compound YbFe$_5$P$_3$, which
resides close to a quantum critical point. The results are compared to the
predictions of scaling laws obtained from a generalized free energy function
expected near an antiferromagnetic quantum critical point (AFQCP). The scaling
behavior depends on the dimensionality $d$ of the fluctuations, the coherence
length exponent $\nu$, and the dynamic exponent $z$. The free energy treats the
magnetic field as a relevant renormalization group variable, which leads to a
new exponent $\phi=\nu z_h$, where $z_h$ is a dynamic exponent expected in the
presence of a magnetic field. When $z_h=z$, $T/H$ scaling is expected, as
observed in several compounds close to a QCP; whereas in YbFe$_5$P$_3$, a
$T/H^{3/4}$ dependence of the scaling is observed. This dependence reflects the
relationship $z_h=(4z/3)$ and a field exponent $\phi =4/3$. A feature of the
scaling law is that it restricts the possible values of the exponents to two
cases for YbFe$_5$P$_3$: $d$=1, $\nu$=1, $z$=1, and $d$=2, $\nu$=1/2, $z$=2.
