Specific heat capacity at $T = T_C$

[augude]

Hi, The project description states that the specific heat capacity for an infinite 2D model behaves as $$C_V \propto |T - T_C(L = \infty)|^{-\alpha},$$ with $\alpha = 0$. What does this even mean? Something raised to the power of $0$ is just $1$? I read in the original paper from Onsager that "The specific heat becomes infinite at this critical point", but I do not get infinite when I substitute $T = T_C$ in the equation above unless I am missing something elementary.

[anderkve]

Hi @augude!

Thanks for asking this question. I thought I had added a note about it in the project description, but apparently I forgot. (Will do so tomorrow.) I'll take some minutes to discuss it in the lecture tomorrow. But the short summary is that "critical exponent = 0" is just the power-law way of saying that it diverges logarithmically. That is, it diverges, but more slowly than any power law with an exponent > 0.

[augude]

Thanks!