Haridev S R: RG studies of scalar-field models of long-range interactions

In this work, we study long-range interactions in non-gravitational field theories and their behaviour in the deep infrared. To model such effects, we consider a nonlocal scalar theory obtained by adding a (\phi \Box^{-1} \phi) term to the local action. Using the functional renormalisation group, we analyse its infrared fixed-point structure.

Within the LPA, we show that nonlocality modifies phase-transition patterns and can induce symmetry breaking. Extending the LPA beyond polynomial truncations, we examine the convexity property of the effective potential as k \to 0 and find that the flow becomes singular for \lambda^2 \gt 0 before reaching the deep infrared.

In the LPA’ framework we find that the infrared-stable fixed point is the nonlocal Gaussian fixed point. We then generalise the model to (\phi \Box^{\sigma/2} \phi) and analyse how the infrared properties depend on \sigma. With appropriate scaling choices, we show that the infrared behaviour remains unchanged up to \sigma = d/2 and follows Sak’s prediction up to \sigma = 2.

Finally, we study higher-derivative cases within the LPA, focusing on \sigma = 4, which corresponds to isotropic Lifshitz criticality, and obtain results consistent with earlier work.