Stability of φ^{4}-vector model: Four-loop ε expansion study

• Published in: Physical review. E Vol. 107; no. 2-1; p. 024133
• Main Authors: Adzhemyan, L Ts, Kudlis, A
• Format: Journal Article
• Language: English
• Published: United States 01.02.2023
• ISSN: 2470-0053
• DOI: 10.1103/PhysRevE.107.024133

In most papers, φ^{4}-field theory with the vector (d-component) field φ_{α} is considered as a particular case of the n-component field model for n=d and O(n) symmetry. However, in such a model the symmetry O(d) admits an addition to the action of a term proportional to the squared divergence of the field ∼h(∂_{α}φ_{α})^{2}. From the point of view of renormalization group analysis, it requires a separate consideration, because it may well change the nature of the critical behavior of the system. Therefore, this frequently neglected term in the action requires a detailed and accurate study on the issue of the existence of new fixed points and their stability. It is known that within the lower order of perturbation theory the only infrared stable fixed point with h=0 exists but the corresponding positive value of stability exponent ω_{h} is tiny. This led us to analyze this constant in higher orders of perturbation theory by calculating the four-loop renormalization group contributions for ω_{h} in d=4-2ɛ within the minimal subtraction scheme, which should be enough to infer positivity or negativity of this exponent. The value turned out to be undoubtedly positive, although still small even in higher loops: 0.0156(3). These results cause the corresponding term to be neglected in the action when analyzing the critical behavior of the O(n)-symmetric model. At the same time, the small value of ω_{h} shows that the corresponding corrections to the critical scaling are significant in a wide range.