Constraint effective action and critical correlation functions at fixed magnetization

Abstract

We present an extension of the functional renormalization group (FRG) framework developed to compute critical probability distributions of the order parameter to momentum-dependent observables. Focusing on the constraint effective action at fixed magnetization for the Ising universality class, we derive its exact flow equations and solve them at the second order of the derivative expansion (DE2). We solve these flow equations numerically for two- and three-dimensional systems, extract universal rate functions and momentum-dependent correlation functions, and benchmark them against Monte Carlo simulations. In three dimensions, we recover the rate function and accurately reproduce the first few Fourier modes of the constrained correlation function and demonstrate the convergence of the method. In two dimensions, the lowest order approximations such as local potential approximation (LPA) fail, and it is required to consider at least the DE2 to describe the critical point. Our results are in qualitative agreement with the numerics. We confirm the robustness of the FRG approach for calculating both zero- and finite-momentum critical observables at fixed magnetization.

17 pages, 7 figures, 1 table. Final version

References in corpus (19)

• The nonperturbative functional renormalization group and its applications
• Precision Islands in the Ising and $O(N)$ Models
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Optimization of the derivative expansion in the nonperturbative renormalization group
• A new method to solve the Non Perturbative Renormalization Group equations
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
• Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model
• High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model
• Generalization of the Central Limit Theorem to Critical Systems: Revisiting Perturbation Theory
• Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the Two-Dimensional Ising Model
• Universal and non-universal large deviations in critical systems
• Critical Probability Distributions of the order parameter at two loops I: Ising universality class
• Constraint correlation functions of the one-dimensional Ising model in the scaling limit
• Critical Probability Distributions of the order parameter at two loops II: $O(n)$ universality class