Related papers: Field Theory, Critical Phenomena and Interfaces
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum…
In this work I show that a simple Field Theory on a non trivial gauge background may behave as a phantom field and contribute to an effective $w<-1$ state equation fluid contribution to cosmology.
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field…
We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i)…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
The framework of Modern Theory of Critical State Transitions considers the relation between different levels of organization in complex systems in terms of Critical State Transitions. A State Transition between levels entails changes of…
These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…
We examine hydrodynamics from the perspective of an effective field theory. The microscopic scale in this case is the thermalization scale, and the macroscopic scale is the gradient, with thermal fluctuations playing the role of $\hbar$. We…