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Two-loop $\beta$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the…
The two-level correlation function $R_{d,\beta}(s)$ of $d$-dimensional disordered models ($d=1$, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ($\beta=1$)…
We renormalize six dimensional phi^3 theory in the modified minimal subtraction (MSbar) scheme at four loops. From the resulting beta-function, anomalous dimension and mass anomalous dimension we compute four loop critical exponents…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the…
We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric…
In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in…
The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop beta function and anomalous dimension eta of the field for the O(N) symmetric scalar theory. The standard perturbative…
We propose an implicit regularisation scheme. The main advantage is that since no explicit use of a regulator is made, one can in principle avoid undesirable symmetry violations related to its choice. The divergent amplitudes are split into…
We analyze the universal features of the critical behaviour of frustrated spin systems with noncollinear order. By means of the field theoretical renormalization group approach, we study the 3d model of a frustrated magnet and obtain…
We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $\beta_t$ in the disordered and ordered phase. Our…
A recent rank 4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory [arXiv:1111.4997 [hep-th]]. The model is built out of $\phi^6$ ($\phi^6_{(1/2)}$), $\phi^4$…
The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic…
We consider defect operators in scalar field theories in dimensions $d=4-\epsilon $ and $d=6-\epsilon$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the…
Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless…
The semi-analytical expression for the forth coefficient of the renormalization group $\beta$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the three-loop…
We propose an all-orders beta function for current-current interactions in 2d with flavor anisotropy. When the number of left-moving and right-moving flavors are unequal, the beta function has a non-trivial fixed point at finite values of…
We recalculate four-loop renormalization group functions in 2-dimensional nonlinear O(n) {\sigma}-model using coordinate-space method. The high accuracy of calculation allow us to find the analytical form of {\beta}- and {\gamma}-function…