Conformal invariance constraints in the O(N) models: A study within the nonperturbative renormalization group

Area of Science:

• * Theoretical physics
• * Statistical mechanics
• * Quantum field theory

Background:

• * Critical phenomena behavior is often invariant under the conformal group.
• * Approximations are necessary for studying critical phenomena, including the functional renormalization group.
• * The derivative expansion is a popular approximation scheme but breaks conformal symmetry at finite orders.

Purpose of the Study:

• * To study constraints from conformal symmetry in O(N) models using the derivative expansion at O(∂²).
• * To minimize conformal symmetry breaking to fix nonphysical parameters in the approximation.
• * To compare critical exponent predictions with the principle of minimal sensitivity.

Main Methods:

• * Employed the derivative expansion at the O(∂²) order within the functional renormalization group framework.
• * Investigated various values of N for the O(N) models.
• * Minimized the breaking of conformal symmetry to determine approximation parameters.

Main Results:

• * Successfully applied conformal symmetry constraints to fix parameters in the O(∂²) derivative expansion.
• * Obtained predictions for critical exponents in O(N) models.
• * Demonstrated a method to mitigate conformal symmetry breaking in approximations.

Conclusions:

• * The study provides a method to improve approximations in critical phenomena by minimizing conformal symmetry breaking.
• * The results offer an alternative approach to calculating critical exponents compared to the principle of minimal sensitivity.
• * This work highlights the importance of conformal symmetry in nonperturbative renormalization group studies.