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Register a new userTruncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
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We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.
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The requirement for the absence of spontaneous symmetry breaking in the d=1 dimension has been used to optimize the regulator dependence of functional renormalization group equations in the framework of the sine-Gordon scalar field theory. Results obtained by the optimization of this kind were compared to those of the Litim-Pawlowski and the principle of minimal sensitivity optimization scenarios. The optimal parameters of the compactly supported smooth (CSS) regulator, which recovers all major types of regulators in appropriate limits, have been determined beyond the local potential approximation, and the Litim limit of the CSS was found to be the optimal choice.
We study the renormalization group flow of $mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed points of the renormalization group flow of these models, which emerge as scaling solutions. In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimension they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution. We also include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method. For each solution we offer new techniques to compute the spectrum of the deformations and obtain the corresponding critical exponents.
In this paper we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank 3 tensorial group field theory. This complete truncation includes non-melonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of non-melonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the non-melonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work.
We apply the functional renormalization-group (FRG) equation to analyze the nature of the QCD critical point beyond the mean-field approximation by taking into consideration the fact that the soft mode associated with the QCD critical point is a linear combination of fluctuations of the chiral condensate and the quark-number density, rather than the pure chiral fluctuations. We first construct an extended quark-meson model in which a new field corresponding to quark-number density is introduced to the conventional one composed of the chiral fields sigma, pi and the quarks. The fluctuations of the quark-number density as well as the chiral condensate are taken into account by solving the FRG equation which contains sigma and the new field as coupled dynamical variables. It is found that the mixing of the two dynamical variables causes a kind of level repulsion between the curvature masses, which in turn leads to an expansion of the critical region of the QCD critical point, depending on the coupling constants in the model yet to be determined from microscopic theories or hopefully by experiments.
We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.
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