Asymmetry of Critical Exponents of O(N) Model due to Spontaneous Symmetry Breaking

It has widely been believed that the critical exponents are equivalent above and below the second-order phase transition point. On the contrary, we show that asymmetry develops in the critical exponents of the O(N) symmetric model due to spontaneous symmetry breaking. Whereas only the four-point vertices are relevant in the symmetric phase, three-point vertices also become relevant in the ordered phase. One of the authors recently formulated a functional renormalization group that can reduce the number of the renormalization parameters to analyze the ordered phase[1]. Using this method to the O(N) symmetric model, we show numerically that the three-point vertices are finite at the fixed point in the ordered phase. Around the fixed point, we also find that the critical exponent of the correlation length has a value different from that of the isotropic fixed point in the symmetric phase. Our mechanism for the emergence of asymmetry in critical exponents is different from the one proposed recently[2].

[1]T. Kita, J. Phys. Soc. Jpn. 88, 054003 (2019).

[2]F. Léonard and B. Delamotte, Phys. Rev. Lett. 115, 200601 (2015).