Related papers: Critical exponents from five-loop scalar theory re…
We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<\zeta<1$, rendering the…
We recalculate the contributions of individual six loop graphs to the $\beta$-function for a three dimensional scalar theory with an arbitrary sextic scalar potential. Previously this was calculated by Hager who specialised to a theory with…
Effective field theories provide a suitable framework for both particle physics and statistical physics. We delve deeper into the study of the effective three-dimensional scalar field theory for its application to statistical physics,…
Using the one-loop Coleman-Weinberg effective potential, we derive a general analytic expression for all the derivatives of the effective potential with respect to any number of classical scalar fields. The result is valid for a…
High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…
The large N limit of the hermitian matrix model in three and four Euclidean space-time dimensions is studied with the help of the approximate Renormalization Group recursion formula. The planar graphs contributing to wave function, mass and…
We study a five dimensional Horava-Lifshitz like scalar QED with dynamical exponent z=2. Consistency of the renormalization procedure requires the presence of four quartic and one six-fold scalar couplings besides the terms bilinear in the…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
The field-theoretical renormalization group approach is used to estimate the universal critical value g_6^* of renormalized sextic coupling constant for the two-dimensional Ising model. Four-loop perturbative expansion for g_6 is calculated…
We present three-loop formulas for the additive renormalization constant A(u,epsilon) and associated renormalization group function B(u) for the specific heat of the O(n) symmetric phi^4 model. Using this result, we obtain also the…
The renormalization group approach in three dimensions is used to estimate the universal critical value g_6^* of the dimensionless sextic effective coupling constant for the Ising model. The four-loop RG expansion for g_6 is calculated and…
The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the…
We analyze the Landau-Wilson field theory with $\text{U}(n)\times\text{U}(m)$ symmetry which describes the finite-temperature phase transition in QCD in the limit of vanishing quark masses with $n=m=N_f$ flavors and unbroken anomaly at the…
The asymptotic structure of the QCD perturbative relation between the on-shell and $\overline{\rm{MS}}$ heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First,…
The coefficient of the dimensionally regularized two-loop R^3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced…
We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$,…
Coupling constant renormalization is investigated in 2 dimensional sigma models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter…