Related papers: Critical Exponents from Field Theory: New Evaluati…
Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
With the help of variational perturbation theory we continue the renormalization constants $\phi^4$-theories in $4- \epsilon$ dimensions to strong bare couplings $g_0$ and find their power behavior in $g_0$, thereby determining all critical…
The autonomous renormalization of the O(N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system…
We point out that the recently developed strong-coupling theory enables us to calculate the three main critical exponents nu, eta, omega, from the knowledge of only the two renormalization constants Z_phi of wave function and Z_m of mass.…
We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents eta, nu, and omega at the both the leading and second…
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell…
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper…
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…
The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale dependent thermodynamic potential at finite temperature and density in the…
We consider the critical behaviour of long-range $O(n)$ models ($n \ge 0$) on ${\mathbb Z}^d$, with interaction that decays with distance $r$ as $r^{-(d+\alpha)}$, for $\alpha \in (0,2)$. For $n \ge 1$, we study the $n$-component…
The critical behavior of $U(n)$-$\chi^{4}$-model with antisymmetric tensor order parameter at charged regime is studied by means of the field theoretic renormalization group at the leading order of $\varepsilon$-expansion (one-loop…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
In this paper we elaborate on the translation-invariant renormalizable Phi^4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and…
The critical behavior of the random-field Ising model has been a puzzle for a long time. Different theoretical methods predict that the critical exponents of the random-field ferromagnet in D dimensions are the same as in the pure…
The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function…
Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…
We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing…
We study the critical behaviour of symmetric $\phi^4_4$ theory including irrelevant terms of the form $\phi^{4+2n}/\Lambda_0^{2n}$ in the bare action, where $\Lambda_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for…
We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric $\vp^4$ theory. From only…