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I would like to understand the reason behind the vanishing critical mass exponents. I've written a program that calculates the fixed points and then the eigenvalues corresponding to the fixed point solutions by substituting them into the Jacobian matrix where each term is composed of the partial derivatives of the beta functions with respect to the dimensionless couplings.

In d=3 scalar phi^4 model, I had no problem obtaining the critical exponents until N=5 but for N=6,7,8 I got just the trivial solutions due to the coupling fixed points being only zeros then for N=9 I got a sensible result for the critical exponent. I wonder whats happening between N=6 to N=8.

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  • $\begingroup$ By "critical mass exponent," are you referring to the critical exponent $\nu$? This cannot be zero by definition. Its value for the $d=3$ O($N$) models is known do fairly good accuracy. $\endgroup$ Commented Nov 18, 2019 at 0:46
  • $\begingroup$ Yes I'm referring to the critical exponent v. What I meant is that by using wegner-houghton equation, between N=6 to 10 I get the coupling fixed points as all zeros or so close to zero. Which once its substituted into the matrix to get the eigenvalues and consequently the exponents, it results with the same values but still N=11, 12, 14 gives around 0.69 which are close to the one obtained for N=5. (above mentioned N's in the question were obtained by using a different regulator) $\endgroup$
    – Monopole
    Commented Nov 22, 2019 at 15:06

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