We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.
The critcal exponent $ω$ is evaluated at $O(1/N)$ in $d$-dimensions in the Gross-Neveu model using the large $N$ critical point formalism. It is shown to be in agreement with the recently determined three loop $β$-functions of the Gross-Neveu-Yukawa model in four dimensions. The same exponent is computed for the chiral Gross-Neveu and non-abelian Nambu-Jona-Lasinio universality classes.
We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of app…
We calculate CFT data for the Gross-Neveu model in $2<d<4$ dimensions at the next-to-leading order in the $1/N$ expansion. In particular, we make use of the background field method to derive various conformal triangles involving the composite operator $s^2$, for the Hubbard-Stratonovich field $s$. We then apply these conformal triangles to obtain the corresponding OPE coefficients.
We calculate the critical exponents $ω_\pm$ in the $d$-dimensional Gross-Neveu model in $1/N$ expansion with $1/N^2$ accuracy. These exponents are related to the slopes of the $β$-functions at the critical point in the Gross - Neveu - Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations.
We compute the anomalous dimensions of a class of operators of the form $(\barψψ)^p$ and $(\barψψ)^pψ$ to leading order in $ε$ in the Gross-Neveu model in $2+ε$ dimensions. We use the techniques developed in arXiv: 1505.00963.
The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.
We calculate the anomalous dimensions of higher-spin currents, both singlet and non-singlet, in the Gross-Neveu model at the $1/n^2$ order. It was conjectured that in the critical regime this model is dual to a higher-spin gauge theory on $AdS_4$. The $AdS/CFT$ correspondence predicts that the masses of higher-spin fields correspond to the scaling dimensions of the singlet currents in the Gross-Neveu model.
We use the large $N$ critical point formalism to compute $d$-dimensional critical exponents at several orders in $1/N$ in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a particular symmetry group or taking the abelian limit of the final exponents recovers known results but also provides expressions for any Lie group or fermion representation.
We use the critical point large $N$ formalism to calculate the critical exponents corresponding to the fermion mass operator and flavour non-singlet fermion bilinear operator in the universality class of Quantum Electrodynamics (QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in $d$-dimensions. The $ε$ expansion of the exponents in $d$ $=$ $4$ $-$ $2ε$ dimensions are in agreement with recent three and four loop perturbative evaluations of both renormalization group functions of these operators. Estimates of the value of the non-singlet operator exponent in three dimension…
We consider a version of the Gross-Neveu model in 1+1 dimensions with discrete chiral and continuous flavor symmetry (isospin). In 2+1 dimensions, this model is known as chiral Heisenberg Gross-Neveu model. Spontaneous symmetry breaking and the emergence of two massless and one massive scalar bosons are shown. A duality to the Nambu--Jona-Lasinio model with isospin is exhibited, provided that the isovector pseudoscalar mean field is constrained to a plane in isospin space. This enables us to find the phase diagram as a function of temperature, chemical potential and isospin chemical potential …
We present N-soliton solutions for the classical (1+1)-dimensional Gross-Neveu model which satisfy non-zero boundary conditions. These solutions are obtained by direct method using some properties of the soliton matrices that appear in the framework of the Cauchy matrix approach.
We reconsider the two-flavor version of the massive, chiral Gross-Neveu model in 1+1 dimensions. Its phase diagram as a function of baryon chemical potential, isospin chemical potential and temperature has previously been explored. We recapitulate the results, adding the missing tricritical curves. They can be determined exactly by extending the standard stability analysis, using fourth order almost degenerate perturbation theory. Results for three different bare masses are presented and discussed.
This paper presents a case study of the effects of increasing the order of a Ginzburg-Landau type expansion, by using the well known Gross-Neveu model in 1+1 dimensions as a test case. It is found that as the order of expansion increases, the predicted phase diagram increasingly resembles the known exact phase diagram. Finally, some properties of arbitrary large order phase diagrams are examined.
The Gross-Neveu model with ${\rm U}_L(N_f)\times{\rm U}_R(N_f)$ chiral symmetry is reconsidered in the large $N_c$ limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The ($x,t$)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.
Renormalization of the Orientable Non-commutative Gross-Neveu Model
我们证明了二维Moyal平面上的非对易Gross-Neveu模型对所有阶都是可重整化的。尽管有剩余的UV/IR混合，但可以实现重整化。然而，在大质量的情况下，这迫使我们引入一个形式为“psibar i gamma^{0} gamma^{1} psi”的附加反项。无质量的情况下，没有这样的加法是可重整化的。
We compute a variational approximation to the entanglement entropy for states of the Gross-Neveu model. Further, we examine the functional dependence of the entanglement entropy on the coupling and number of colors in the theory. Our results display non-peturbative behavior. It is shown that the entanglement entropy is monotonically decreasing and convex with respect to the coupling. We also show how the behavior of the entanglement entropy under renormalization group transformations is related to the beta function of the Gross-Neveu model, and compare these renormalization group results to ou…
The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade appr…
