# Is there any model in statistical physics which has the ratio of specific heat exponent to correlation length exponent, $\alpha/\nu \approx 2.44$?

I am simulating a disordered ising-like model in 2d whose phase transition is expected to be continuous, whose universality class is as yet unknown. By plotting the Specific heat scaling function, i.e., $C L^{-\alpha/\nu}$ vs $tL^{1/\nu}$, I find that the ratio ($\alpha/\nu$) is $\approx 2.44$. Is there a previously studied universality class which has this value for $\alpha/\nu$ ?

• what is the accuracy and the precision of this simulation ? – sailx Jul 18 '14 at 18:49
• This data comes from an "exact" recursive method for L=7 to L=12. So, the system sizes are indeed quite small. However, $\alpha / \nu$ can be tuned to the 2nd decimal digit for a good scaling collapse of this data. So, I would bet on atleast the first decimal digit. – Srivatsan Balakrishnan Jul 19 '14 at 3:04

I made a very simple mistake of plotting Specific heat and not Specific heat per spin. It is specific heat per spin that scales as $L^{\alpha/\nu}$. And hence, the actual value from the data of my previous simulations is $2.44-2 = 0.44$. Using system sizes $10$ and $12$, one in fact gets a value $0.3$.