Related papers: Renormalization Group and Probability Theory
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
The renormalization group method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
Continuous phase transitions in equilibrium statistical mechanics were successfully described 50 years ago with the development of the renormalization group framework. This framework was initially developed in the context of phase…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly…
The vulcanization transition - the crosslink-density-controlled equilibrium phase transition from the liquid to the amorphous solid state - is explored analytically from a renormalization group perspective. The analysis centers on a minimal…
We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…
We aim here to show that reductionism and emergence play a complementary role in understanding natural processes and in the dynamics of science explanation. In particular, we will show that the renormalization group - one of the most…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive…
We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the…
This lecture provides an introduction to the renormalisation group as applied to scattering of two nonrelativistic particles. As well as forming a framework for constructing effective theories of few-nucleon systems, these ideas also…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…