  Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic
geometry. By using the thermodynamic extrinsic curvature, one may obtain a more
complete geometric representation of the critical phenomena and thermodynamics.
We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two
dimensional gas of anyons. Using extrinsic curvature, we find new fixed points
in nonperturbative thermodynamics of the anyon gas that particles behave as
semions. Here, we investigate the critical behavior of thermodynamic extrinsic
curvature of two-dimensional Kagome Ising model near the critical point $
\beta_{c} =({{k_{B} T_{c}}})^{-1}$ in a constant magnetic field and show that
it behaves as $ \left| {\beta- \beta_{c} } \right|^{\alpha} $ with $ \alpha=0
$, where $ \alpha $ denotes the critical exponent of the specific heat. Then,
we consider the three dimensional spherical model and show that the scaling
behavior is $ \left| {\beta- \beta_{c} } \right|^{\alpha} $ , where $ \alpha
=-1 $. Finally, using a general argument, we show that extrinsic curvature $ K
$ have two different scaling behaviors for positive and negative $ \alpha $.
For $\alpha> 0$, our results indicate that $ K \sim \left|{\beta- \beta_{c} }
\right|^{{\frac{1}{2}} (\alpha-2)} $. However, for $ \alpha <0$, we found a
different scaling behavior, where $ K\sim \left| {\beta- \beta_{c} }
\right|^{\alpha} $.
